Question 1.
\nFive students obtained 10, 20, 30, 40, and 50 marks respectively, What would be the mean,
\n(a) 35
\n(b) 25
\n(c) 30
\n(d) 40
\nAnswer:
\n(c) 30<\/p>\n
![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/KSEEB-Solutions.png\")
<\/p>\n
Question 2.
\n…………… = \\(\\frac{\\Sigma X}{N}\\) is concerned with
\n(a) Arithmetic mean
\n(b) Mode
\n(c) Median
\n(d) Geometric mean
\n(a) Arithmetic mean<\/p>\n
Question 3.
\nThe most commonly used measure of central tendency is
\n(a) Mode
\n(b) Arithmetic mean
\n(c) Median
\n(d) Percentile
\nAnswer:
\n(b) Arithmetic mean<\/p>\n
Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. II. Fill in the blanks<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. III. Match the following<\/span><\/p>\n IV. Answer the following questions in one word or sentence<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. V. Answer the following Questions in about four sentences<\/span><\/p>\n Question 1. Question 2. The measure of central tendency is needed to evaluate the relative economic condition. It is a way of summarizing the data in the form of atypical or representative values.<\/p>\n Question 3. Question 4. (b) Income of 7 families per week Rs. 550, 490,670,890,435, 590,575 Question 5. Question 6. Question 7. For example, if we have secured 91 percentile in Economics final examination, that means your position is below 9 percent of the total candidates who had appeared in the examination.<\/p>\n Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. The following formula is used to calculate mode for a continuous series: Question 14. VI. Answer the following Questions in about twelve sentences.<\/span><\/p>\n Question 1. <\/p>\n (b) Assumed mean method. Question 2. Question 3. Question 4. It gives importance to a particular variable while calculating the arithmetic mean. It is calculated with the help of the following formula: Question 5. (a) Arithmetic mean: It is the most commonly used measure of central tendency. It is defined as the sum of the values of all the observations divided by the number of observations. The arithmetic mean can be calculated through the direct method, assumed mean method, and step deviation methods. In each method, a different formula is used.<\/p>\n (b) Median: It is that positional value of the variable which divides the distribution into two equal parts, one part comprises all the values greater than or equal to the median value and the other comprises all values less than or equal to it.<\/p>\n Median is considered as the middle element when the data set is arranged in order of magnitude. It can be easily computed b sorting the data from smallest to largest and counting the middle value,<\/p>\n If there are even numbers in the data. there will be two observations that fall in the middle. The median in this case is computed as the arithmetic mean of the middle values.<\/p>\n In order to calculate the median, it is important to know the position of the median i.e. item at which the median falls. The position of the median can be calculated by the following formula:<\/p>\n Median = Size of \\(\\frac{(n+1)^{\\text {th }}}{2}\\) item.<\/p>\n (C) Mode: The word mode is derived from the French word la Mode which means most fashionable values of a distribution. It is the value that is repeated the highest number of times in the series. So mode is the most frequently observed data value. It is indicated by M0.<\/p>\n For continuous series, Mode is calculated with the help of the following formula: Question 6. Question 7. Mediam = 35.5th item i.e. 60 Question 8. Question 9. In discrete series, we may come across unimodal, bimodal, and multimodal. For instance: In the series 12, 13, 14, 12, 15, 12, the number 12 has appeared maximum times so it is called unimodal.<\/p>\n Bimodal: In case there are two values that have appeared an equal highest number of times in the given observations, then it is called bimodal.<\/p>\n For instance: In the series 10, 11, 12, 10, 12, 10, 13, 14, 12, the observations 10 and 12 have appeared maximum times, so it is bimodal.<\/p>\n Multimodal: If in given observations, there are more than two observations appeared in the highest numbers then it is called multimodal.<\/p>\n For instance in the series 10, 11, 12. 12, 11, 10, 30, 40, there three values that have occurred more times.<\/p>\n Question 10. The first or lower quartile is denoted by Q1<\/sub>, the second quartile or median is denoted by Q2<\/sub> and the third quartile or upper quartile is denoted by Q3<\/sub>.<\/p>\n The first quartile is calculated with the help of following fonnula: The second quartile is calculated with the help of following fonnula: The third quartile is calculated with the help of following forumula: The method for locating the quartile is the same as that of the median in the case of individual and discrete series.<\/p>\n Question 11. As stated above, there are 99 percentiles for frequency distribution. These percentiles divide the distribution into hundred equal parts in between two consecutive percentiles, one percent of the value exists.<\/p>\n VII. Answer the following in about twenty sentences<\/span><\/p>\n Question 1. Question 2. (b) Step Deviation Method: Question 3. Question 4. Question 5. Question 6. i.e., 2nd item + 0.75 (3rd item – 2\u2019 item) Calculate of Q2<\/sub>: Question 7. From the above table, we can locate 25 – 30 as a modal group as it has occurred maximum times. L = Lower limit of modal class. Question 8. VIII. Project-oriented Question<\/span><\/p>\n Question 1. Ranges = Laigest – Smallest = 35 – 25 Mean temperature of the day Question 1. (b) Average performance of students in a class (c) Average production in a factory per shift. (d) Average wage in an industrial concern. (e) When the sum of absolute deviations from average is the least. (f) When quantities of the variable are in ratios. (g) In the case of open-ended frequency distribution. Question 2. (ii) Which average is affected the most by the presence of extreme items? (iii) The algebraic sum of deviation of a set of n values from the arithmetic mean is Question 3. (ii) An average alone is not enough to compare series. (iii) Arithmetic mean is a positional value. (iv) Upper quartile is the lowest value of the top 25% of items. (v) Median is unduly affected by extreme observations. Multiple Choice Questions with Answers<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Very Short Answers Type Questions with Answers<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Karnataka 1st PUC Economics Question Bank Chapter 5 Measures of Central Tendency 1st PUC Economics Measures of Central Tendency TextBook Questions and Answers I. Choose the correct Answer Question 1. Five students obtained 10, 20, 30, 40, and 50 marks respectively, What would be the mean, (a) 35 (b) 25 (c) 30 (d) 40 Answer: …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/87752"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=87752"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/87752\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=87752"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=87752"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=87752"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nWhich of the following represent median?
\n(a) Q1<\/sub>
\n(b) Q4<\/sub>
\n(c) Q3<\/sub>
\n(d) Q2<\/sub>
\nAnswer:
\n(d) Q2<\/sub><\/p>\n
\nPercentiles divide the distribution equally into
\n(a) 100 parts
\n(b) 25 pasts
\n(c) 75 parts
\n(d) 50 parts
\nAnswer:
\n(a) 100 parts<\/p>\n
\nQuartiles are the measures that divide the data into
\n(a) 2 equal parts
\n(b) 1 equal part
\n(C) 4 equal parts
\n(d) 3 equal parts
\nAnswer:
\n(c) 4 equal parts<\/p>\n<\/p>\n
\nThe sum of the deviations about mean is
\n(a) Zero
\n(b) One
\n(c) Niinirnum
\n(d) Maximum
\nAnswer:
\n(a) Zero<\/p>\n
\nAssigning weights to various items according to their importance is called
\n(a) Arithmetic mean
\n(b) Weighted arithmetic mean
\n(c) Median
\n(d) Mode
\nAnswer:
\n(b) Weighted Arithmetic Mean<\/p>\n
\nMedian divides the distribution
\n(a) Into two equal parts
\n(b) 1st part is more than 2nd part
\n(c) Into unequal parts
\n(d) 2nd part is more than 1st part
\nAnswer:
\n(a) Into two equal parts<\/p>\n
\nThe middle value of an ordered series is called
\n(a) Median
\n(b) Weighted mean
\n(c) Mean
\n(d) Mode
\nAnswer:
\n(a) Median<\/p>\n
\nWhich of the following is the formula for measuring median?
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-43.png\")
\nAnswer:
\n(b) Size of \\(\\frac{(\\mathrm{N}+1)^{t h}}{2}\\) item<\/p>\n<\/p>\n
\nWhat would be the median wage for the following wages of 5 laborers 10, 20, 30, 35, 38?
\n(a) Rs. 20
\n(b) Rs. 25
\n(c) Rs. 10
\n(d) Rs. 30
\nAnswer:
\n(d) Rs. 30<\/p>\n
\nThe word \u2018mode\u2019 has been derived from
\n(a) Latin
\n(b) French
\n(c) English
\n(d) German
\nAnswer:
\n(b) French<\/p>\n
\nThe shoe size of most of the people in India is No.7. Which measure of central value does it represent?
\n(a) Mean
\n(b) Median
\n(c) Quartile
\n(d) Mode
\nAnswer:
\n(d) Mode<\/p>\n<\/p>\n
\nThe median is always between
\n(a) The arithmetic mean and the mode
\n(b) Quartiles and median
\n(c) Mode and median
\n(d) Percentiles and quartiles
\nAnswer:
\n(a) Tire arithmetic mean and the mode<\/p>\n
\nIn discrete series……..formula is used to calculate the arithmetic mean.
\nAnswer:
\n\\(\\frac{\\Sigma X}{N}\\)<\/p>\n
\n……arithmetic mean gives relative importance to each item.
\nAnswer:
\nWeighted<\/p>\n
\n3rd quartile and percentile are the same.
\nAnswer:
\n75%<\/p>\n
\nThere are…………..quartiles in a series.
\nAnswer:
\n3<\/p>\n
\nA measure that divides the series into hundred equal parts is called
\nAnswer:
\nPercentiles<\/p>\n
\nMedian can be easily located through………..
\nAnswer:
\nCumulative frequency<\/p>\n
\nFor studying phenomena like intelligence and honesty……….. is a better average
\nAnswer:
\nMode<\/p>\n<\/p>\n
\n…….is not affected by extreme values.
\nAnswer:
\nMedian<\/p>\n
\nThe most frequently observed value in a series is called
\nAnswer:
\nMode<\/p>\n
\nA distribution with more than two modes is called
\nAnswer:
\nBimodal<\/p>\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.1.png\")
\nAnswer:
\n1-d. 2-c. 3-g. 4-c. 5-f. 6-a. 7-b. 8-i. 9-j. 10-h.<\/p>\n<\/p>\n
\nWhat is meant by central tendency?
\nAnswer:
\nCentral tendency is one of the statistical tools that summarize the data in a single value in such a way that this single value can represent the entire data.<\/p>\n
\nWhat is the meaning of arithmetic mean?
\nAnswer:
\nArithmetic mean is defined as the sum of the values of all observations divided by the number of observations.<\/p>\n
\nName any two partition values.
\nAnswer:
\nQuartiles and percentiles.<\/p>\n
\nDefine median.
\nAnswer:
\nThe median is the middle element when the data set is arranged in order of magnitude.<\/p>\n
\nPocket money of 8 students is Rs. 6,12,18, 24, 30, 36,42 and 48. Calculate the mean. The sum of all the observations is sigma \u03a3X=215.
\nAnswer:
\nX\u0304 = \\(\\frac{\\Sigma X}{N}=\\frac{216}{8}\\) = 27<\/p>\n
\nWrite the relative positions of mean, median, and mode.
\nAnswer:
\nWM = \\(\\frac{\\Sigma W X}{\\Sigma W}\\)<\/p>\n<\/p>\n
\nWrite the relative positions of mean, median, and mode.
\nAnswer:
\nMe<\/sub> > M1<\/sub> > Mo<\/sub><\/p>\n
\nWhich partition value divides the total set of values into four equal parts?
\nAnswer:
\nQuartiles.<\/p>\n
\nA shoe manufacturing company manufactures shoes only for adults. As the company wants to know the most popular size, which type of central tendency will be the most appropriate?
\nAnswer:
\nMode.<\/p>\n
\nWhat do you mean by percentiles?
\nAnswer:
\nPercentiles are those measures that divide the distribution into hundred equal parts.<\/p>\n
\nGive the meaning of quartiles.
\nAnswer:
\nQuartiles are the measures that divide the data into four equal parts, where each portion contains an equal number of observations.<\/p>\n
\nWhat type of central tendency is suitable to describe qualitative data?
\nAnswer:
\nMode.<\/p>\n
\nWhat is unimodal?
\nAnswer:
\nIf we get a unique value of mode, then it is called unimodal.<\/p>\n<\/p>\n
\nCalculate the mode from the following data:
\n8,10, 6, 4,12,10, 8,10,18,16, 10,18, 10, 10.
\nAnswer:
\n10 is the mode as it has the occurred maximum number of tunes.<\/p>\n
\nWhat are the types of measures of central tendency?
\nAnswer:
\nThere are three types of measures of central tendency i.e. mean, median, and mode.<\/p>\n
\nWhat is a central tendency? Why do we need it?
\nAnswer:
\nThe central tendency is one of the statistical tools which summarizes the data in a single value in such a way that this single value can represent the entire data.<\/p>\n
\nWrite the merits of the arithmetic mean.
\nAnswer:
\nThe following are the merits of arithmetic mean:<\/p>\n\n
\nCalculate the arithmetic mean from the following data.
\n(a) Marks obtained by 10 students
\n30,62,47, 25, 52,39,56, 66,12, 24.
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.2.png\")
<\/p>\n<\/p>\n
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.3.png\")
<\/p>\n
\nWhy is the arithmetic mean the most commonly used measure of central tendency?
\nAnswer:
\nArithmetic mean is considered as the most commonly used average among all the measures of central tendency. Tins are mainly because it is simple to calculate and it is based tending into account all the observations.<\/p>\n
\nWhat does weighted arithmetic mean? Give its formula.
\nAnswer:
\nWhile calculating the arithmetic means, sometimes, it is essential to give weightage to various items according to their importance. For example, there are two commodities oranges and radish. You are interested in finding the average price of oranges and radish. We may give importance to the rise in the price of oranges for which weights are to be given. To calculate the average of both the products we use weighted arithmetic mean.<\/p>\n
\nWrite a note on percentile.
\nAnswer:
\nPercentiles are the statistical tools used to measure the values by dividing the distribution into hundred equal parts so that we can get 99 dividing positions.<\/p>\n
\nWhat is a quartile? Give the formula to find out Q3.
\nAnswer:
\nQuantiles are the measures that divide the given data into four equal parts, where each portion contains an equal number of observations.<\/p>\n<\/p>\n
\nWhat is the median? How do you compute it?
\nAnswer:
\nMedian is that positional value of the variable which d\u00ed ides the distribution into two equal parts. It is the middle clement when the data set is arranged in order of the magnitudes.
\nMedian can be computed with the help of following formula,
\nMedian = Size of \\(\\frac{(\\mathrm{N}+1)^{t h}}{2}\\) item.<\/p>\n
\nCalculate the value of the median (S – 2018)
\n5,7,9, 12,11,8,7, 15, 25.
\nAnswer:
\nWe need to put in ascending order
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.4.png\")
<\/p>\n
\nCalculate lower quartile
\nX: 22, 26, 14, 30, 18, 11, 35, 41, 12, 32
\nAnswer:
\nFirst, we need to write in an ascending order
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.5.png\")
<\/p>\n
\nHow do you classify modal series?
\nAnswer:
\nThe mode can be classified as follows:
\n(a) Uni-modal
\n(b) Bi-modal
\n(c) Multi-modal.<\/p>\n<\/p>\n
\nWhat is the mode? Give the formula to find out mode in continuous series.
\nAnswer:
\nThe word mode is derived from the French ord la Mode which signifies the most fashionable values of a distribution. because it is repeated the highest number of times in the series. So. mode is the most frequently observed data value,<\/p>\n
\nM0 = L + \\(\\frac{D_{1}}{D_{1}+D_{2}}\\) \u00d7 h<\/p>\n
\nDistinguish between arithmetic mean and weighted mean.
\nAnswer:<\/p>\n\n\n
\n Arithmetic Mean<\/strong><\/td>\n Weighted Mean<\/strong><\/td>\n<\/tr>\n \n Arithmetic mean is defined as the stim of the values of all observations divided by the number of observations<\/td>\n It gives importance to a particular available while calculating the arithmetic mean<\/td>\n<\/tr>\n \n It is generally calculated by \u03a3 X\/N<\/td>\n It is calculated by \\(\\frac{q_{1} p_{1}+q_{2} p_{2}}{q_{1}+q_{2}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nThe daily income often families in a certain locality are given below.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.6.png\")
\nCalculate the arithmetic mean by:
\n(a) Direct method
\n(b) Assumed mean method.
\nAnswer:
\n(a) Direct method
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.7.png\")
<\/p>\n
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.8.png\")
<\/p>\n
\nCalculate the arithmetic mean from the following data.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-9.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.9.png\")
<\/p>\n<\/p>\n
\nCalculate the median from the following data.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-12.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.10.png\")
\nMedian = Value of \\(\\left(\\frac{N+1}{2}\\right)^{t h}\\) item = Value of \\(\\left(\\frac{30+1}{2}\\right)^{\\text {th }}\\) item
\n= Value of \\(\\left(\\frac{31}{2}\\right)^{\\text {th }}\\) item = 15.5th item is 30
\n\u2234 Median = 30<\/p>\n
\nDefine weighted mean. How do you calculate it? Explain.
\nAnswer:
\nWhile calculating the arithmetic means, sometimes, it is essential to give weightage to various items according to their importance. For example, there are two commodities oranges and radish. You are interested in finding the average price of oranges and radish. We may give importance to the rise in the price of oranges for which weights are to be given. To calculate the average of both the products we use weighted arithmetic mean.<\/p>\n
\n\\(\\frac{\\mathrm{q}_{1} \\mathrm{p}_{1}+\\mathrm{q}_{2} \\mathrm{p}_{2}}{\\mathrm{q}_{1}+\\mathrm{q}_{2}}\\)<\/p>\n
\nName and define any three statistical averages.
\nAnswer:
\nThere are several statistical measures of central tendency or averages. The most commonly used averages are these:<\/p>\n\n
<\/p>\n
\nIt is generally calculated by the formula IX\/ N.
\nThe calculation of arithmetic mean can be studied under two broad categories viz.,<\/p>\n\n
\nMo<\/sub> = L + \\(\\frac{D_{1}}{D_{1}+D_{2}}\\) \u00d7 h<\/p>\n<\/p>\n
\nCalculate the Q1<\/sub> and Q3<\/sub> from the following data.
\n22, 26, 14, 30. 18, 11, 35, 41, 12, 32.
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.12.png\")
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.13.png\")
<\/p>\n
\nCalculate the median from the following data.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-17.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-18.png\")
\nMedian = Size of Q3<\/sub> = 32.75 item
\nMedian = Size of \\(\\left(\\frac{70+1}{2}\\right)^{\\mathrm{th}}\\) item
\nMedian = Size of \\(\\left(\\frac{71}{2}\\right)^{\\text {th }}\\) item<\/p>\n
\n\u2234 Median = 60<\/p>\n
\nCalculate the mode from the following data.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-19.png\")
\nAnswer:
\nMode =18 (it has occurred highest i.e., 25 times).<\/p>\n
\nDefine unimodal, bimodal, and multimodal.
\nAnswer:
\nThe word mode is derived from the French word \u2018la Mode\u2019 which means most fashionable values of a distribution. It is the value that is repeated the highest number of times in the series. So Mode is the most frequently observed data value. It is indicated by Mo<\/sub>.<\/p>\n
\nUnimodal: In case there is a unique value of mode, it is called unimodal. Here, there will be only one value that might have occurred the highest times in the series of observations.<\/p>\n<\/p>\n
\nWrite a note on quartiles.
\nAnswer:
\nQuartiles are the measures that divide the data into four equal parts, where each portion contains an equal number of observations. There are three quartiles. They are as follows:<\/p>\n\n
\nQ1<\/sub> = Size of \\(\\frac{(\\mathrm{N}+1)^{\\mathrm{th}}}{4}\\) item.<\/p>\n
\nMedian (Q2<\/sub>) = Size of \\(\\frac{(N+1)^{t h}}{2}\\) item.<\/p>\n
\nQ3<\/sub> = Size of \\(\\frac{3(\\mathrm{~N}+1)^{\\mathrm{th}}}{4}\\) item.<\/p>\n<\/p>\n
\nWrite a note on percentiles.
\nAnswer:
\nPercentiles are tire values that divide the distribution into hundred equal parts. So we can get 99 dividing positions denoted by P1<\/sub>. P2<\/sub>, P3<\/sub>…….. P99<\/sub>, P50 <\/sub>is the median value. If we have secured the 82 percentile in an IAS entrance examination, it means that our position is below 18% of the total candidates who had appeared in the entrance examination.<\/p>\n
\nCalculate the arithmetic mean by direct, assumed mean and step deviation methods for the following data.
\n40, 50, 55, 78, 58.
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.15.png\")
\nDirect method:
\nx\u0304 = \\(\\frac{\\Sigma x}{N}=\\frac{281}{5}\\)
\nx\u0304 = 56.2
\nAssumed mean method:
\nx\u0304 = A + \\(\\frac{\\Sigma d}{\\mathrm{~N}}\\)
\n= 40 + \\(\\frac{81}{5}\\)
\n= 40 + 16.2
\nx\u0304 = 56.2
\nStep deviation method:
\nx\u0304 = A + \\(\\frac{\\Sigma d^{\\prime}}{\\mathrm{N}}\\) \u00d7 c
\n= 40 + \\(\\frac{8.1}{5}\\) \u00d7 10
\n= 40 + 1.62 \u00d7 10
\n= 40 + 16.2
\nx\u0304 = 56.2<\/p>\n<\/p>\n
\nCalculate the average marks of the following students using:
\n(a) Direct method
\n(b) Step deviation method.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-21.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.17.png\")
\n(a) Direct Method:
\nx\u0304 = \\(\\frac{\\Sigma f x}{N}=\\frac{2110}{70}\\) = 30.14<\/p>\n
\nx\u0304 = A + \\(\\frac{\\Sigma d^{\\prime}}{\\mathrm{N}}\\) \u00d7 c
\n= 5 + \\(\\frac{176}{70}\\) \u00d7 10
\n= 5 + 2.514 \u00d7 10
\n= 5 + 25.14
\nx\u0304 = 30.14<\/p>\n
\nThe following data relates to the daily wages of persons working in a factory. Compute the median daily wages.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-23.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.18.png\")
![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.19.png\")
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-25.png\")
\nM = 33.71
\nwhere L – Lower limit
\nCF – cumulative frequency of preceding median
\nF – Frequency of median
\nI – Magnitude of median class.<\/p>\n<\/p>\n
\nFind the median of the following data.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-26.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.20.png\")
<\/p>\n
\nCalculate the Q1<\/sub> Q2<\/sub>, and Q3<\/sub> front the following data
\n15, 21, 26, 30, 40, 45, 50, 54, 60, 65, 70.
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.21.png\")
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.22.png\")
<\/p>\n
\nCalculate the Q1<\/sub> Q2<\/sub> and Q3<\/sub> from the following data.
\n22, 26, 14, 30, 18, 11, 35, 41, 12, 32. (Board Paper)
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.23.png\")
<\/p>\n
\nQ = 12 + 0.75 (14 – 12) = 12 + 0.75 (2) = 12 + 1.5
\nQ1<\/sub> = 13.51<\/p>\n<\/p>\n
\n
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.24.png\")
<\/p>\n
\nCalculate the value of a worker family\u2019s is daily modal income from the following data.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-37.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.25.png\")
<\/p>\n
\nTo find exact mode, the following formula is used:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.26.png\")
<\/p>\n
\nD1<\/sub> = Difference between frequency of the model class and frequency of preceding modal class.
\nD2<\/sub> = Difference between frequency of the modal class and frequency of succeeding modal class.
\nh = Class interval of the distribution.<\/p>\n
\nCalculate the mode from the following distribution. (S – 2018)
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency-40.png\")
\nAnswer:
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.27.png\")
\nBy seeing the frequency column, we can make out that the class interval 30-40 is considered as the modal group. To find out the exact mode the following formula is used.
\n![\"1st](\"https:\/\/kseebsolutions.guru\/wp-content\/uploads\/2021\/06\/1st-PUC-Economics-Question-Bank-Chapter-5-Measures-of-Central-Tendency.28.png\")
<\/p>\n
\nAs per the recorded temperature, every two hours in a day from 6 am to 6 pm calculate the range and mean temperature of the day.<\/p>\n\n\n
\n Hours<\/strong><\/td>\n Temperature<\/strong><\/td>\n<\/tr>\n \n 6 – 8 am<\/td>\n 25\u00b0 celsius<\/td>\n<\/tr>\n \n 8 – 10 am<\/td>\n 26\u00b0 celsius<\/td>\n<\/tr>\n \n 10 – 12 am<\/td>\n 28\u00b0 celsius<\/td>\n<\/tr>\n \n 12 – 2 pm<\/td>\n 34\u00b0 celsius<\/td>\n<\/tr>\n \n 2 – 4 pm<\/td>\n 35\u00b0 celsius<\/td>\n<\/tr>\n \n 4 – 6 pm<\/td>\n 30\u00b0 celsius<\/td>\n<\/tr>\n \n <\/td>\n 178<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nRange = 10\u00b0 ceLsius<\/p>\n
\nx\u0304 = \\(\\frac{\\Sigma x}{\\mathrm{~N}}=\\frac{178}{6}\\)
\nx\u0304 = 29.66
\nN = Number of observation
\n\u03a3x = Sum of temperatures during the day
\nThe mean temperature of the day is 29.66\u00b0 Celsius.<\/p>\n<\/p>\n1st PUC Economics Measures of Central Tendency Additional Questions and Answers<\/h3>\n
\nWhich average would be suitable in the following cases?
\n(a) Average size of readymade garments.
\nAnswer:
\nMode<\/p>\n
\nAnswer:
\nMedian<\/p>\n
\nAnswer:
\nArithmetic mean<\/p>\n
\nAnswer:
\nArithmetic mean<\/p>\n
\nAnswer:
\nArithmetic mean<\/p>\n
\nAnswer:
\nMedian<\/p>\n
\nAnswer:
\nMedian<\/p>\n<\/p>\n
\nIndicate the most appropriate alternative from the multiple choices provided against each question.
\n(i) The most suitable average for qualitative measurement is
\n(a) Arithmetic mean
\n(b) Median
\n(c) Mode
\n(d) Geometric mean
\n(e) None of these
\nAnswer:
\n(b) Median<\/p>\n
\n(a) Median
\n(b) Mode
\n(c) Arithmetic mean
\n(d) Geometric mean
\n(e) Harmonic mean
\nAnswer:
\n(c) Arithmetic mean<\/p>\n
\n(a) n
\n(b) 0
\n(c) 1
\n(d) None of these
\nAnswer:
\n(b) 0 .<\/p>\n
\nComment whether the following statements are true or false.
\n(i) The sum of deviation of items from the median is zero.
\nAnswer:
\nFalse. The sum of deviations of items from the median will be minimum and not be zero.<\/p>\n
\nAnswer:
\nTrue. Apart from averages, there are other measurements to compare series.<\/p>\n
\nAnswer:
\nFalse. Itisamathematicalaveragewhichtakesall values in a given observation. Median is positional value.<\/p>\n
\nAnswer:
\nTrue. The upper quartile divides the distribution as 75% of total items fall less than 75 and 25% above 75%.<\/p>\n
\nAnswer:
\nFalse. Median is a positional value. It is not influenced by any extreme values.<\/p>\n
\nMean of 7, 3, 6, 9,0, 5,12,0, 5 is
\n(a) 3.6
\n(b) 5.2
\n(c) 5.6
\n(d) 4.9
\nAnswer:
\n(b) 5.2<\/p>\n
\nThe summation of deviations about the arithmetic mean will be
\n(a) 0
\n(b) 1
\n(c) Highest
\n(d) Lowest
\nAnswer:
\n(a) 0<\/p>\n
\nThe measures of central tendency are also called as:
\n(a) Differentiation
\n(b) rages
\n(c) Integration
\n(d) Integration
\nAnswer:
\n(b) Acres<\/p>\n<\/p>\n
\nThe most widely used average is
\n(a) Medium
\n(b) Mode
\n(c) Arithmetic mean
\n(d) None of these
\nAnswer:
\n(c) Arithmetic mean<\/p>\n
\nThe most frequently occurring value in a series is called
\n(a) Quartiles
\n(b) Median
\n(c) Geometric mean
\n(d) Mode
\nAnswer:
\n(d) Mode<\/p>\n
\nThe mode of 4, 6, 8,5,9, 7,5 is
\n(a) 4
\n(b) 5
\n(c) 9
\n(d) 7
\nAnswer:
\n(b) 5<\/p>\n
\nMedian of 9, 5,8, 4,10,6, 7, 2 is
\n(a) 6
\n(b) 10
\n(c) 2
\n(d) 8
\nAnswer:
\n(a) 6<\/p>\n
\nCF is a short form used for
\n(a) Common value
\n(b) Cumulative frequency
\n(C) Common factor
\n(d) None of the above
\nAnswer:
\n(b) Cumulative frequency<\/p>\n
\nA frequency distribution having two modes is said to be
\n(a) Unimodal
\n(b) Bimodal
\n(c) Trimodal
\n(d) None of these
\nAnswer:
\n(b) Bimodal<\/p>\n
\nThe histogram is useful to determine graphically the value of
\n(a) Mean
\n(b) Median
\n(c) Mode
\n(d) All the above
\nAnswer:
\n(c) Mode<\/p>\n
\nWhat do you mean by the arithmetic mean?
\nAnswer:
\nIt is the sum of all items divided by the number of observations.<\/p>\n
\nWhat would be the sum of deviations of individual items taken from the arithmetic mean?
\nAnswer:
\nZero.<\/p>\n
\nName the appropriate method for the common factor of the deviation of the items.
\nAnswer:
\nStep deviation method.<\/p>\n
\nWhat would you get if the sum of items is divided by their number?
\nAnswer:
\nMean.<\/p>\n
\nHow do you measure arithmetic mean for open-end series?
\nAnswer:
\nIn open-end series, we have to assume that the unknown classes which depend on the pattern of class intervals of other classes.<\/p>\n<\/p>\n
\nWhat is the median?
\nAnswer:
\nMedian is the middle value in the data set when its elements are arranged in sequential order.<\/p>\n
\nWhat do you call the measure which divides the series into four equal parts?
\nAnswer:
\nQuartiles.<\/p>\n
\nShow the relationship between mean, mode, and median.
\nAnswer:
\nMode = 3 median – 2 mean.<\/p>\n
\nName the graph used to locate median graphically
\nAnswer:
\nOgive curve.<\/p>\n
\nName the graph used to compute mode.
\nAnswer:
\nHistogram.<\/p>\n1st PUC Economics Question Bank with Answers<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"