JEE Main & Advanced Mathematics Statistics Question Bank

done Measures of dispersion Total Questions - 38

• question_answer1)
  The measure of dispersion is                                 [DCE 1998]
  A)
                  Mean deviation       done clear
  B)
                  S.D.          done clear
  C)
                  Quartile deviation   done clear
  D)
                  All of these done clear
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• question_answer2)
  The mean deviation from the median is                 [Kurukshetra CEE 1995, 98]
  A)
                  Greater than that measured from any other value               done clear
  B)
                  Less than that measured from any other value done clear
  C)
                  Equal to that measured from any other value       done clear
  D)
                   Maximum if all observations are positive done clear
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• question_answer3)
  The S.D. of 5 scores 1, 2, 3, 4, 5 is                         [AMU 1991; DCE 2000]
  A)
                  \[\frac{2}{5}\]         done clear
  B)
                  \[\frac{3}{5}\]         done clear
  C)
                  \[\sqrt{2}\]             done clear
  D)
                  \[\sqrt{3}\] done clear
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• question_answer4)
  The variance of the data 2, 4, 6, 8, 10 is                [AMU 1992]
  A)
                  6              done clear
  B)
                  7              done clear
  C)
                  8              done clear
  D)
                  None of these done clear
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• question_answer5)
  The mean deviation of the numbers 3, 4, 5, 6, 7 is               [AMU 1993; DCE 1998]
  A)
                  0              done clear
  B)
                  1.2 done clear
  C)
                  5              done clear
  D)
                   25 done clear
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• question_answer6)
  If the standard deviation of 0, 1, 2, 3, ?..,9 is K, then the standard deviation of 10, 11, 12, 13 ?..19 is
  A)
                  K              done clear
  B)
                  K + 10 done clear
  C)
                  \[K+\sqrt{10}\]       done clear
  D)
                  10K done clear
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• question_answer7)
  For a normal distribution if the mean is M, mode is \[{{M}_{0}}\] and median is \[{{M}_{d}}\], then
  A)
                  \[M>{{M}_{d}}>{{M}_{0}}\]    done clear
  B)
                  \[M<{{M}_{d}}<{{M}_{0}}\] done clear
  C)
                  \[M={{M}_{d}}{{M}_{0}}\]      done clear
  D)
                  \[M={{M}_{d}}={{M}_{0}}\] done clear
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• question_answer8)
  For a frequency distribution mean deviation from mean is computed by                                            [DCE 1994]
  A)
                  M.D.\[=\frac{\sum d}{\sum f}\]            done clear
  B)
                  M.D.\[=\frac{\sum fd}{\sum f}\]           done clear
  C)
                  M.D.\[=\frac{\sum f|d|}{\sum f}\]       done clear
  D)
                  M.D.\[=\frac{\sum f}{\sum f|d|}\] done clear
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• question_answer9)
  Quartile deviation for a frequency distribution is  [DCE 1998]
  A)
                  \[Q={{Q}_{3}}-{{Q}_{1}}\]       done clear
  B)
                  \[Q=\frac{1}{2}({{Q}_{3}}-{{Q}_{1}})\] done clear
  C)
                  \[Q=\frac{1}{3}({{Q}_{3}}-{{Q}_{1}})\]   done clear
  D)
                  \[Q=\frac{1}{4}({{Q}_{2}}-{{Q}_{1}})\] done clear
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• question_answer10)
  The variance of the first n natural numbers is      [AMU 1994; SCRA 2001]
  A)
                  \[\frac{{{n}^{2}}-1}{12}\]       done clear
  B)
                  \[\frac{{{n}^{2}}-1}{6}\]         done clear
  C)
                  \[\frac{{{n}^{2}}+1}{6}\]         done clear
  D)
                  \[\frac{{{n}^{2}}+1}{12}\] done clear
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• question_answer11)
  For a moderately skewed distribution, quartile deviation and the standard deviation are related by                [AMU 1996]
  A)
                  S.D.\[=\frac{2}{3}\]Q.D.         done clear
  B)
                  S.D.\[=\frac{3}{2}\]Q.D. done clear
  C)
                  S.D.\[=\frac{3}{4}\]Q.D.         done clear
  D)
                  S.D.\[=\frac{4}{3}\]Q.D. done clear
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• question_answer12)
  For a frequency distribution standard deviation is computed by applying the formula       [Kurukshetra CEE 1999]
  A)
                  \[\sigma =\sqrt{\left( \frac{\sum \,fd}{\sum \,f} \right)-\frac{\sum \,f{{d}^{2}}}{\sum \,f}}\]         done clear
  B)
                  \[\sigma =\sqrt{\frac{\sum \,f{{d}^{2}}}{\sum \,f}-{{\left( \frac{\sum \,f{{d}^{2}}}{\sum \,f} \right)}^{2}}}\] done clear
  C)
                  \[\sigma =\sqrt{{{\left( \frac{\sum \,fd}{\sum \,f} \right)}^{2}}-\frac{\sum \,f{{d}^{2}}}{\sum \,f}}\]             done clear
  D)
                  \[\sigma =\sqrt{\frac{\sum \,f{{d}^{2}}}{\sum \,f}-{{\left( \frac{\sum \,fd}{\sum \,f} \right)}^{2}}}\] done clear
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• question_answer13)
  For a frequency distribution, standard deviation is computed by
  A)
                  \[\sigma =\frac{\sum f(x-\bar{x})}{\sum f}\]       done clear
  B)
                  \[\sigma =\frac{\sqrt{\sum f{{(x-\bar{x})}^{2}}}}{\sum f}\] done clear
  C)
                  \[\sigma =\sqrt{\frac{\sum f{{(x-\bar{x})}^{2}}}{\sum f}}\] done clear
  D)
                  \[\sigma =\sqrt{\frac{\sum f(x-\bar{x})}{\sum f}}\] done clear
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• question_answer14)
  If Q.D. is 16, the most likely value of S.D. will be
  A)
                  24            done clear
  B)
                  42 done clear
  C)
                  10            done clear
  D)
                  None of these done clear
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• question_answer15)
  If M.D. is 12, the value of S.D. will be
  A)
                  15            done clear
  B)
                  12 done clear
  C)
                  24            done clear
  D)
                  None of these done clear
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• question_answer16)
  The range of following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is                                            [DCE 1998]
  A)
                  11            done clear
  B)
                  7 done clear
  C)
                  5.5           done clear
  D)
                  6 done clear
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• question_answer17)
  If v is the variance and s is the standard deviation, then [Kurukshetra CEE 1995]
  A)
                  \[{{v}^{2}}=\sigma \]              done clear
  B)
                  \[v={{\sigma }^{2}}\] done clear
  C)
                  \[v=\frac{1}{\sigma }\]          done clear
  D)
                  \[v=\frac{1}{{{\sigma }^{2}}}\] done clear
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• question_answer18)
  If each observation of a raw data whose variance is \[{{\sigma }^{2}}\], is multiplied by l, then the variance of the new set is [Pb. CET 1993]
  A)
                  \[{{\sigma }^{2}}\] done clear
  B)
                  \[{{\lambda }^{2}}{{\sigma }^{2}}\] done clear
  C)
                  \[\lambda +{{\sigma }^{2}}\] done clear
  D)
                  \[{{\lambda }^{2}}+{{\sigma }^{2}}\] done clear
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• question_answer19)
  For a given distribution of marks mean is 35.16 and its standard deviation is 19.76. The co-efficient of variation is
  A)
                  \[\frac{35.16}{19.76}\]           done clear
  B)
                  \[\frac{19.76}{35.16}\] done clear
  C)
                  \[\frac{35.16}{19.76}\times 100\]         done clear
  D)
                  \[\frac{19.76}{35.16}\times 100\] done clear
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• question_answer20)
  If 25% of the item are less than 20 and 25% are more than 40, the quartile deviation is
  A)
                  20            done clear
  B)
                  30 done clear
  C)
                  40            done clear
  D)
                  10 done clear
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• question_answer21)
  For a normal curve, the greatest ordinate is
  A)
                  2 ps        done clear
  B)
                  \[\sigma \sqrt{2\pi }\] done clear
  C)
                  \[\frac{1}{\sqrt{2\pi \sigma }}\]            done clear
  D)
                  \[\frac{1}{\sigma \sqrt{2\pi }}\] done clear
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• question_answer22)
  If the variance of observations \[{{x}_{1}},\,{{x}_{2}},\,......{{x}_{n}}\] is \[{{\sigma }^{2}}\], then the variance of \[a{{x}_{1}},\,a{{x}_{2}}.......,\,a{{x}_{n}}\], a ¹ 0 is
  A)
                  \[{{\sigma }^{2}}\] done clear
  B)
                  \[a\,{{\sigma }^{2}}\] done clear
  C)
                  \[{{a}^{2}}{{\sigma }^{2}}\]   done clear
  D)
                  \[\frac{{{\sigma }^{2}}}{{{a}^{2}}}\] done clear
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• question_answer23)
  The mean deviation from the mean for the set of observations ?1, 0, 4 is
  A)
                  \[\sqrt{\frac{14}{3}}\]            done clear
  B)
                  2 done clear
  C)
                  \[\frac{2}{3}\]         done clear
  D)
                  None of these done clear
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• question_answer24)
  The mean and S.D. of 1, 2, 3, 4, 5, 6 is
  A)
                  \[\frac{7}{2},\,\sqrt{\frac{35}{12}}\]     done clear
  B)
                  3, 3 done clear
  C)
                  \[\frac{7}{2},\,\sqrt{3}\]        done clear
  D)
                  \[3,\,\frac{35}{12}\] done clear
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• question_answer25)
  The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be                                   [DCE 1995]
  A)
                  40            done clear
  B)
                  45 done clear
  C)
                  \[40+\frac{21}{25}\] done clear
  D)
                  None of these done clear
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• question_answer26)
  The S.D of 15 items is 6 and if each item is decreased or increased by 1, then standard deviation will be                 [Pb. CET 1994,98]
  A)
                  5              done clear
  B)
                  7              done clear
  C)
                  91/15      done clear
  D)
                  6 done clear
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• question_answer27)
  The quartile deviation for the following data is

  x :	2	3	4	5	6
  f :	3	4	8	4	1

                                  [AMU 1988; Kurukshetra CEE 1999]
  A)
                  0              done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{2}\]         done clear
  D)
                  1 done clear
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• question_answer28)
  The sum of squares of deviations for 10 observations taken from mean 50 is 250. The co-efficient of variation is [DCE 1996]
  A)
                  50%         done clear
  B)
                  10%         done clear
  C)
                  40%         done clear
  D)
                  None of these done clear
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• question_answer29)
  The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are                                              [AMU 1994]
  A)
                  2 and 9    done clear
  B)
                  3 and 8    done clear
  C)
                  4 and 7    done clear
  D)
                  5 and 6 done clear
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• question_answer30)
  Consider any set of observations \[{{x}_{1}},\,{{x}_{2}},\,.{{x}_{3}},.\,...,{{x}_{101}}\]; it being given that \[{{x}_{1}}<{{x}_{2}}<{{x}_{3}}<....<{{x}_{100}}<{{x}_{101}}\]; then the mean deviation of this set of observations about a point k is minimum when k equals                                   [DCE 1997]
  A)
                  \[{{x}_{1}}\]            done clear
  B)
                  \[{{x}_{51}}\] done clear
  C)
                  \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] done clear
  D)
                  \[{{x}_{50}}\] done clear
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• question_answer31)
  For (2n+1) observations \[{{x}_{1}},\,-{{x}_{1}}\], \[{{x}_{2}},\,-{{x}_{2}},\,.....{{x}_{n}},\,-{{x}_{n}}\] and 0 where x?s are all distinct. Let S.D. and M.D. denote the standard deviation and median respectively. Then which of the following is always true [Orissa JEE 2002]
  A)
                  S.D. < M.D. done clear
  B)
                  S.D. > M.D. done clear
  C)
                  S.D. = M.D. done clear
  D)
                  Nothing can be said in general about the relationship of S.D. and M.D. done clear
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• question_answer32)
  Suppose values taken by a variable x are such that \[a\le {{x}_{i}}\le b\], where \[{{x}_{i}}\] denotes the value of x in the ith case for i = 1, 2, n. Then          [Kurukshetra CEE 1995, 2000]
  A)
                  \[a\le \text{Var}(x)\le b\]      done clear
  B)
                  \[{{a}^{2}}\le \text{Var}(x)\le {{b}^{2}}\] done clear
  C)
                  \[\frac{{{a}^{2}}}{4}\le \text{Var}(x)\]  done clear
  D)
                  \[{{(b-a)}^{2}}\ge \text{Var}(x)\] done clear
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• question_answer33)
  The variance of a, b and g is 9, then variance of 5a, 5b and 5g is                                                       [AMU 1998]
  A)
                  45            done clear
  B)
                  9/5 done clear
  C)
                  5/9          done clear
  D)
                  225 done clear
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• question_answer34)
  A batsman scores runs in 10 innings 38, 70, 48, 34, 42, 55, 63, 46, 54, 44, then the mean deviation is [Kerala  Engg. 2002]
  A)
                  8.6           done clear
  B)
                  6.4 done clear
  C)
                  10.6         done clear
  D)
                  9.6 done clear
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• question_answer35)
  What is the standard deviation of the following series [DCE 1996]

  Measurements	0-10	10-20	20-30	30-40
  Frequency	1	3	4	2

  A)
                  81            done clear
  B)
                  7.6 done clear
  C)
                  9              done clear
  D)
                  2.26 done clear
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• question_answer36)
  In an experiment with 15 observations on x, the following results were available \[\sum {{x}^{2}}=2830\], \[\sum x=170\]. On observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is       [AIEEE 2003]
  A)
                  78.00       done clear
  B)
                  188.66 done clear
  C)
                  177.33     done clear
  D)
                  8.33 done clear
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• question_answer37)
  The quartile deviation of daily wages (in Rs.) of 7 persons given below 12, 7, 15, 10, 17, 19, 25 is [Pb. CET 1991, 96; Kurukshetra CEE 1997]
  A)
                  14.5        done clear
  B)
                  5 done clear
  C)
                  9              done clear
  D)
                  4.5 done clear
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• question_answer38)
  Karl-Pearson?s coefficient of skewness of a distribution is 0.32. Its S.D. is 6.5 and mean 39.6. Then the median of the distribution is given by                                        [Kurukshetra CEE 1991]
  A)
                  28.61      done clear
  B)
              38.81 done clear
  C)
                  29.13       done clear
  D)
                  28.31 done clear
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