{"id":35214,"date":"2022-08-25T11:20:59","date_gmt":"2022-08-25T05:50:59","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=35214"},"modified":"2022-08-25T11:20:59","modified_gmt":"2022-08-25T05:50:59","slug":"inter-2nd-year-maths-2a-measures-of-dispersion-important-questions","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/inter-2nd-year-maths-2a-measures-of-dispersion-important-questions\/","title":{"rendered":"Inter 2nd Year Maths 2A Measures of Dispersion Important Questions"},"content":{"rendered":"

Students get through Maths 2A Important Questions<\/a> Inter 2nd Year Maths 2A Measures of Dispersion Important Questions which are most likely to be asked in the exam.<\/p>\n

Intermediate 2nd Year Maths 2A Measures of Dispersion Important Questions<\/h2>\n

Question 1.
\nFind the mean deviation about the median for the data 4, 6, 9, 3, 10, 13, 2 (AP Mar. ’17) (TS. Mar. ’15 )
\nSolution:
\nGiven ungrouped data are 4, 6, 9, 3, 10, 13, 2
\nExpressing the data in the ascending order of magnitude, we have 2, 3, 4, 6, 9, 10, 13
\n\u2234 Median = 6 b (say)
\nThe absolute values are
\n|6 – 2|, |6 – 3|, |6 – 4|, |6 – 6|, |6 – 9|, |6 – 10|, |6 – 13| = 4, 3, 2, 0, 3, 4, 7
\n\"Inter<\/p>\n

Question 2.
\nFind the mean deviation from the mean of the following discrete data 6, 7, 10, 12, 13, 4, 12, 16. (Mar. ’14)
\nSolution:
\nThe A.M. of the given data \\(\\bar{x}\\) = \\(\\frac{6+7+10+12+13+4+12+16}{8}\\) = \\(\\frac{80}{8}\\) = 10
\nThe absolute values of th\u00e9 deviations are
\n|6 – 10|, |7 – 10|, |10 – 10|, |12 – 10|, |13 – 10|, |4 – 10|, |12 – 10|, |16 – 10|
\n= 4, 3, 0, 2, 3, 6, 2, 6
\n\u2234 The mean deviation from the mean = \\(\\frac{1}{n} \\sum_{i=1}^{n}\\left|x_{i}-\\bar{x}\\right|\\)
\n= \\(\\frac{1}{8}\\) (4 + 3 + 0 + 2 + 3 + 6 + 2 + 6) = \\(\\frac{26}{8}\\) = 3.25<\/p>\n

Question 3.
\nFind the variance and standard deviation of the following data 5, 12, 3, 18, 6, 8, 2, 10 (A.P. Mar. ’15)
\nSolution:
\nA. M. = \\(\\bar{x}\\) = \\(\\frac{\\Sigma x_{i}}{n}\\) = \\(\\frac{5+12+3+18+6+8+2+10}{8}\\) = \\(\\frac{64}{8}\\) = 8
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 4.
\nFind the mean deviation about the mean for the following data 3, 6, 10, 4, 9, 10 (TS Mar. \u201917)
\nSolution:
\nThe arithmetic mean of the given data
\n\"Inter<\/p>\n

Question 5.
\nFind the mean deviation about the median for the data 13, 17, 16, 11, 13, 10, 16, 11, 18, 12, 17. (AP. Mar. ’16)
\nSolution:
\nGiven ungrouped data are
\n13, 17, 16, 11, 13, 10, 16, 11, 18, 12, 17
\nExpressing the data in the ascending order of magnitude, we have
\n10, 11, 11, 12, 13, 13, 16, 16, 17, 17, 18
\n\u2234 Median = 13 = b(say)
\nThe absolute values are
\n|13 – 10|, |13 – 11|, |13 – 11|, |13 – 12|, |13 – 13|, |13 – 13|, |13 – 16|, |13 – 16|, |13 – 17|, |13 – 17|, |13 – 18|
\n= 3, 2, 2, 1, 0, 0, 3, 3, 4, 4, 5
\nMean deviation from the median
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 6.
\nFind the mean deviation about the mean for the following data. (AP Mar. \u201815)
\n\"Inter
\nSolution:
\nConstruct the table
\n\"Inter<\/p>\n

Question 7.
\nFind the mean deviation about the mean of the following data (AP Mar. ’17, ’16)
\n\"Inter
\nSolution:
\nTaking the assumed mean a = 25 and h = 10
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 8.
\nFind the variance and standard deviation of the following data
\n\"Inter
\nSolution:
\nConstruct the table
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 9.
\nCalculate the variance and standard deviation of the following continuous frequency distribution.
\n\"Inter
\nSolution:
\nLet assumed mean A = 65
\nThen yi<\/sub> = \\(\\frac{x_{i}-65}{10}\\)
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 10.
\nFind the mean deviation from the mean of the following data using step deviation method. (AP Mar. ’16)
\n\"Inter
\nSolution:
\nLet assumed mean A = 35
\nThen di<\/sub> = \\(\\frac{x_{i}-35}{10}\\)
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 11.
\nFind the mean deviation from the mean of the following discrete data 6, 7, 10, 12, 13, 4, 12, 16. (Mar – 2014)
\nSolution:
\nThe A.M. of the given data \\(\\bar{x}\\) = \\(\\frac{6+7+10+12+13+4+12+16}{8}\\)
\n= \\(\\frac{80}{8}\\) = 10
\nThe absolute values of the deviations are
\n|6 – 10|, |7 – 10|, |10 – 10|, |12 – 10|, |13 – 10|, |4 – 10|, |12 – 10|, |16 – 10| = 4, 3, 0, 2, 3, 6, 2, 6
\n\"Inter<\/p>\n

Question 12.
\nFind the mean deviation from the median of discrete data 6, 7, 10, 12, 13, 4, 12, 16
\nSolution:
\nGiven data points are 6, 7, 10, 12, 13, 4, 12, 16
\nExpressing the data points in the ascending order of magnitude 4, 6, 7, 10, 12, 12, 13, 16
\n\u2234 Median = \\(\\frac{10+12}{2}\\) =11
\nThe absolute values of the deviations are
\n|11 – 4|, |11 – 6|, |11 – 7|, |11 – 10|, |11 – 12|, |11 – 12|, |11 – 13|, |11 – 16|
\n= 7, 5, 4, 1, 1, 1, 2, 5
\n\u2234 Mean deviation from the median = \\(\\frac{1}{8}\\)(7 + 5 + 4 + 1 + 1 + 1 + 2 + 5)
\n= \\(\\frac{26}{8}\\) = 3.25<\/p>\n

\"Inter<\/p>\n

Question 13.
\nFind the mean about the mean for the following data.
\n\"Inter
\nSolution:
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 14.
\nFind the mean deviation from the median for the following data
\n\"Inter
\nSolution:
\nGiven observations in the ascending order, we get the following distribution.
\n\"Inter
\nMedian of these observations = 13
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 15.
\nFind the mean deviation about the mean for the following data (A.P. Mar. ’15)
\n\"Inter
\nSolution:
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 16.
\nFind the mean deviation about the median for the following data (A.P. Mar. ’16)
\n\"Inter
\nSolution:
\nTaking the assumed mean a = 25 and h = 10
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

Question 17.
\nFind the mean deviation about the median for the following data
\n\"Inter
\nSolution:
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 18.
\nFind the variance and standard deviation of the following data 5, 12, 3, 18, 6, 8, 2, 10 (A.P. Mar. ’15)
\nSolution:
\n\"Inter
\n\"Inter<\/p>\n

Question 19.
\nFind the variance and standard deviation of the following data
\n\"Inter
\nSolution:
\nConstruct the table
\n\"Inter<\/p>\n

Question 20.
\nCalculate the variance and standard deviation of the following continuous frequency distribution. (Mar. 2014)
\n\"Inter
\nSolution:
\nLet assumed mean A = 65
\nThen yi<\/sub> = \\(\\frac{x_{i}-65}{10}\\)
\nConstruct the table
\n\"Inter
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 21.
\nStudents of two sections A and B of a class show the following performance in a test (conducted for 100 marks)
\n\"Inter
\nWhich section of students has greater variability in performance?
\nSolution:
\nIn section \u2014 A variance or the distribution \\(\\sigma_{1}^{2}\\) = 64
\n\u21d2 S.D. \u03c31<\/sub> = 8
\nIn section \u2014 8 variance of the distrib\u00f9tion \\(\\sigma_{2}^{2}\\) = 81
\n\u21d2 S.D. \u03c32<\/sub> = 9
\nSince the average marks of both sections of students is the same i.e., 45
\n\u2234 The section with greater S.D. will have more variability. Hence section B has greater variability in the performance.<\/p>\n

Question 22.
\nLives of two models or refrigerators A and B obtained in a survey are given below:
\n\"Inter
\nWhich refrigerator model would you suggest to purchase?
\nSolution:
\nFirst to find the mean and variance of the lives of model A and Model B of refrigerators.
\nConstruct the table.
\n\"Inter
\n\"Inter
\n\"Inter
\nSince C.V. of model B < C.V. of model A
\n\u2234 Model B is more consistent than the model A with regard to life in years.
\nHence we suggest Model B for purch.<\/p>\n

Question 23.
\nFind the mean deviation from the mean of the following data using step deviation method.
\n\"Inter
\n(T.S. Mar. \u201816)
\nSolution:
\nLet assumed mean A = 35
\nThen di<\/sub> = \\(\\frac{x_{i}-35}{10}\\)
\nConstruct the table
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 24.
\nThe following table gives the daily wages of workers in a factory. Compute the standard deviation and the co-efficient of variation of the wages of the workers.
\n\"Inter
\nSolution:
\nTo solute this problem using the step deviation method.
\nHere h = 50
\nLet assumed mean A = 300
\nThen yi<\/sub> = \\(\\frac{x_{i}-300}{50}\\)
\nConstruct the table
\n\"Inter
\n\"Inter
\n\"Inter<\/p>\n

Question 25.
\nAn analysis or monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following data.
\n\"Inter
\ni) Which firm A or B. has greater variability in industrial wages?
\nii) Which firm has large wage bill?
\nSolution:
\n\"Inter
\n\u2234 firm B has greater variability in industrial wages.<\/p>\n

ii) Total wages paid to the workers in firm
\nA = 500 \u00d7 186
\n= 93,000
\nTotal wages paid to the workers in form
\nB = 600 \u00d7 175
\n= 1,05,000
\nHence firm B has larges wage bill.<\/p>\n

Question 26.
\nThe variance of 20 observations in 5. If each of the observation is multiplied by 2, find the variance of the resulting observations.
\nSolution:
\nLet x1<\/sub>, x2<\/sub> …, x20<\/sub> be the given observations and \\(\\bar{x}\\) be their mean.
\nGiven n = 20 and variance = 5
\n\"Inter
\nSubstituting the values of xi<\/sub> and in (1), we get
\n\"Inter
\n\u2234 The variance of the resulting observations = \\(\\frac{1}{20}\\) \u00d7 400 = 20
\n= 22<\/sup> \u00d7 5<\/p>\n

\"Inter<\/p>\n

Question 27.
\nIf each of the observations x1<\/sub>, x2<\/sub> ….. xn<\/sub> is increased by k, where k is a positive or negative number, then show that the variance remains unchanged.
\nSolution:
\nLet \\(\\overline{\\bar{x}}\\) be the mean of x1<\/sub>, x2<\/sub> …. xn<\/sub>. Then their variance is given by \\(\\sigma_{1}^{2}\\) = \\(\\frac{1}{n} \\sum_{i=1}^{n}\\left(x_{i}-\\bar{x}\\right)^{2}\\)
\nIf to each observation we add a constant k, then the new (changed) observations will be yi<\/sub> = xi<\/sub> + k
\n\"Inter
\nThus the variance of the new observations is the same as that of the original observations.<\/p>\n

Question 28.
\nThe scores of two cricketers A and B in 10 innings are given below. Find who is a better run getter and who \u00a1s a more consistent player.
\n\"Inter
\n\"Inter
\n\"Inter
\n\"Inter
\nCricketer A is a better run getter
\nSince C.V. of A < C.V. of B
\nHence cricketer A is a more consistent players.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students get through Maths 2A Important Questions Inter 2nd Year Maths 2A Measures of Dispersion Important Questions which are most likely to be asked in the exam. Intermediate 2nd Year Maths 2A Measures of Dispersion Important Questions Question 1. Find the mean deviation about the median for the data 4, 6, 9, 3, 10, 13, …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[14],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35214"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=35214"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35214\/revisions"}],"predecessor-version":[{"id":35215,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35214\/revisions\/35215"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=35214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=35214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=35214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}