{"id":120689,"date":"2022-05-11T17:48:20","date_gmt":"2022-05-11T12:18:20","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=120689"},"modified":"2022-05-11T17:48:20","modified_gmt":"2022-05-11T12:18:20","slug":"chapter-6-measures-of-dispersion-questions-and-answers-ncert-solutions-for-class-11-economicsstatistics-for-economics","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/education\/chapter-6-measures-of-dispersion-questions-and-answers-ncert-solutions-for-class-11-economicsstatistics-for-economics","title":{"rendered":"Chapter 6 – Measures of Dispersion Questions and Answers: NCERT Solutions for Class 11 Economics(Statistics for Economics)"},"content":{"rendered":"

Question 1.
\nA measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.<\/h2>\n

Answer:
\nDispersion is the extent to which values in a distribution differ from the avarage of the distribution. Knowledge of only average is insufficient as it does not reflect the quantum of variation in values.
\nMeasures of dispersion enhance the understanding of a distribution considerably by providing information about how much the actual value of items in a series deviate from the central value, e.g., per capita income gives only the average income but a measure of dispersion can tell you about income inequalities, thereby improving the understanding of the relative living standards of different sections of the society. Through value of dispersion one can better understand the distribution.
\nThus a measure of dispersion is a good supplement to the central value in understanding a frequency distribution.<\/h3>\n

Question 2.
\nWhich measure of dispersion is the best and how?<\/h2>\n

Answer:
\nStandard Deviation is considered to be the best measure of dispersion and is therefore the most widely used measure of dispersion.
\nIt is based on all values and thus provides information about the complete series. Because of this reason, a change in even one value affects the value of standard deviation.
\nIt is independent of origin but not of scale.
\nIt is us\u2019eful in advanced statistical calculations like comparison of variability in two data sets.
\nIt can be used in testing of hypothesis.
\nIt is capable of further algebraic treatment.<\/h3>\n

Question 3.
\nSome measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?<\/h2>\n

Answer:
\nYes, it is true that some measures of dispersion depend upon the spread of values, whereas some calculate the variation of values from the central value. Range and Quartile Deviation measure the dispersion by calculating the spread within which the value lie. Mean Deviation and Standard Deviation calculate the extent to which the values differ from the average or the central value.<\/h3>\n

Question 4.
\nIn town, 25% of the persons earned more than \u20b9 45,000 whereas 75% earned more than 18,000. Calculate the absolute and relative values of dispersion.<\/h2>\n

Answer:
\n25% of the persons earned more than \u20b9 45,000. This implies that upper quartile Q3= 45,000 75% earned more than 18,000. This implies that lower quartile Q1=18,000
\nAbsolute Measure of Dispersion = Q3\u2013 Q1= 45,000 \u2013 18,000 = 27,000
\nRelative Measure of Dispersion
\nCo-efficient of Quartile Deviation<\/h3>\n

\"\"<\/p>\n

Question 5.
\nThe yield of wheat and rice per acre for 10 districts of a state is as under<\/h2>\n

\"\"<\/p>\n

Calculate for each crop,
\n(i) Range
\n(ii) QD
\n(iii) Mean\u2019Deviation about Mean
\n(iv) Mean Deviation about Median
\n(v) Standard Deviation
\n(vi) Which crop has greater variation?
\n(vii) Compare the value of different measures for each crop.<\/h2>\n

Answer:
\n(i) Range
\n(a) Wheat Highest value of distribution (H) = 25
\nLowest value of distribution (L) = 9
\nRange = H \u2013 L = 25 \u2013 9 = 16
\n(b) Rice Highest value of distribution (H) = 34
\nLowest value of distribution (L)=12
\nRange = H \u2013 L = 34 \u2013 12 = 22
\n(ii) Quartile Deviation
\n(a) Wheat Arranging the production of wheat in increasing order 9, 10, 10, 12, 15, 16, 18, 19, 21, 25
\nQ1=N+14th item =10+14th item =114th item
\n= 2.75th item
\n= Size of 2nd item + 0.75 (size of 3rd item \u2013 size of 2nd item)
\n= 10 + 0.75(10 \u2013 10)
\n= 10 + 0.75 \u00d7 0
\n= 10
\nQ3=3(N+1)4th item =3(10+1)4th item
\n=334th item = 8.25th
\n= Size of 8th item + 0.25 (size of 9th item \u2013 size of 8th item)
\n= 19 + 0.25(21 \u2013 19)
\n= 19 + 0.25 \u00d7 2
\n= 19 + 0.50 = 19.50
\nQuartile Deviation =Q3\u2212Q12=19.50\u2212102=9.502= 4.75
\n(b) Rice Arranging the data of production of rice
\n12, 12, 12, 15, 18, 18, 22, 23, 29, 34 item
\nQ1=N+14th item =10+14th item
\n= 2.75 th item
\n= Size of 2nd item + 0.75 (size of 3rd item \u2013 size of 2nd item)
\n= 12 + 0.75(12 \u2013 12) = 12 + 0.75 \u00d7 0
\n= 12<\/h3>\n

\"\"<\/p>\n

= 8.25th item
\n= Size of 8th item + 0.25 (size of 9th item \u2013 size of 8th item)
\n= 23 + 0.25(29 \u2013 23)
\n= 23 + 0.25 \u00d7 6
\n= 23 + 1.5
\n= 24.5
\nQuartile Deviation =Q3\u2212Q12=24.5\u2212122=12.502= 6.25
\n(iii) Mean Deviation about Mean
\n(a) Wheat<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

(b) Rice<\/h3>\n

\"\"<\/p>\n

(iv) Mean Deviation about Median
\n(a) Wheat<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

(b) Rice<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

(v) Standard Deviation
\n(a) Wheat<\/h3>\n

\"\"<\/p>\n

(b) Rice<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

(vi) Coefficient of Variation
\n(a) Wheat
\nCV =\u03c3X\u00af\u00af\u00af\u00af\u00af\u00d7100=5.0415.5\u00d7100= 32.51
\n(b) Rice
\nCV =\u03c3X\u00d7100=7.1619.5\u00d7100= 36.71
\nRice crop has greater variation as the coefficient of variation is higher for rice as compared to that of wheat.
\n(vii) Rice crop has higher Range, Quartile Deviation, Mean Deviation about Mean, Mean Deviation about Median, Standard Deviation and Coefficient of Variation.<\/h3>\n

Question 6.
\nIn the previous question, calculate the relative measures of variation and indicate the value which , in your opinion, is more reliable.<\/h2>\n

Answer:
\n(i) Coefficient of Range
\n(a) Wheat<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

The coefficient of variation is more reliable than all other measures.<\/h3>\n

Question 7.
\nA batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their scores in five previous scores which are<\/h2>\n

\"\"<\/p>\n

Which batsman should be selected if we want,
\n(i) a higher run-getter, or
\n(ii) a more reliable batsman in the team?<\/h2>\n

Answer:
\nBatsman X<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

(i) Average of Batsman X is higher than that of Batsman Y, so he should be selected if we want a high scorer.
\n(ii) The Batsman Y is more reliable than Batsman X. This is because the coefficient of variation of Batsman X is higher than that of Batsman Y.<\/h3>\n

Question 8.
\nTo check the quality of two brands of light bulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.<\/h2>\n

\"\"<\/p>\n

(i) Which brand gives higher life?
\n(ii) Which brand is more dependable?<\/h2>\n

Answer:
\nFor Brand A<\/h3>\n

\"\"<\/p>\n

For Brand B<\/h3>\n

\"\"<\/p>\n

\"\"<\/p>\n

(i) The average life of bulb of Brand B is comparatively higher than that of Brand A.
\n(ii) The bulbs of Brand B are more dependable as CV of Brand B is lesser than CV of Brand A.<\/h3>\n

Question 9.
\nAverage daily wage of 50 workers of a factory was \u20b9 200 with a Standard Deviation of \u20b9 40. Each worker is given a raise of \u20b9 20. What is the new average daily wage and standard deviation? Have wages become more or less uniform?<\/h2>\n

Answer:
\nN = 50
\nx\u00af\u00af\u00af= 200
\n\u03c3 = 40
\nAverage wage =Total wagesNumber of workers
\n200 =Total wages50
\nSo, total wages = 200 \u00d7 50 = \u20b9 10,000
\nNow, increase in wage rate = \u20b920
\nTotal raise = 50 \u00d7 20= \u20b9 1,000
\nTotal wage after raise = \u20b9 10,000 + 1,000 = \u20b9 11,000
\nNew average wage =New total wagesNumber of workers=11,00050= \u20b9220
\nThus, Mean increases by the amount of increase in wage of each worker as the absolute increase was equal for all.
\nStandard Deviation will remain the same that is \u20b940 as Standard Deviation is independent of origin and hence addition of equal amount in all the values will not cause any change in the Standard Deviation.
\nUniformity of wages can be seen by coefficient of variation.
\nPreviously, the coefficient of variation was
\nCV =\u03c3X\u00af\u00af\u00af\u00af\u00af\u00d7100= (40\/200) \u00d7 100 = 20
\nThe new coefficient of variation after wage increase is given by
\nCV =\u03c3x\u00d7100= (40\/220) \u00d7 100 = 18.18
\nThis shows that wages have become more uniform now as the new CV is lower.<\/h3>\n

Question 10.
\nIf in the previous question, each worker is given a hike of 10% in wages, how are the Mean and Standard Deviation values affected?<\/h2>\n

Answer:
\nAverage wage = \u20b9 200
\nHike in wages = 10%
\nSince arithmetic mean is not independent of scale, the mean will also increase by 10%.
\n=10100\u00d7200= \u20b9 20
\nHence, the new Mean will be
\n200 + 20 = \u20b9 220
\nStandard Deviation is also not independent of scale, hence, the Standard Deviation will also increase by 10% Initial Standard Deviation = \u20b9 40
\nSo, New Standard Deviation = \u20b940 +10% of 40
\n= \u20b9 (40 + 4)
\n= \u20b9 44<\/h3>\n

Question 11.
\nCalculate the Mean Deviation using Mean and Standard Deviation for the following distribution.<\/p>\n

\"\"<\/p>\n

Answer:<\/p>\n

\"\"<\/p>\n

Question 12.
\nThe sum of 10 values is 100 and the sum of their squares is 1090. Find out the coefficient of variation.<\/h2>\n

Answer:<\/h3>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

Class 11 Economics(Statistics for Economics) NCERT book solutions for Chapter 6 – Measures of Dispersion Questions and Answers.<\/p>\n","protected":false},"author":21830,"featured_media":120395,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":{"0":"post-120689","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-education"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/120689","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=120689"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/120689\/revisions"}],"predecessor-version":[{"id":120721,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/120689\/revisions\/120721"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/120395"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=120689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=120689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=120689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}