JEE Main & Advanced Mathematics Statistics Question Bank

done Mock Test - Statistics Total Questions - 25

• question_answer1)
  The mean of a set of numbers is \[\bar{X}\]if each number is divided by 3, then the new mean is
  A)
  \[\bar{X}\]         done clear
  B)
  \[\bar{X}+3\] done clear
  C)
  \[3\bar{X}\]                   done clear
  D)
  \[\frac{{\bar{X}}}{3}\] done clear
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• question_answer2)
  The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is
  A)
  2                      done clear
  B)
  2.57 done clear
  C)
  3                      done clear
  D)
  3.75 done clear
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• question_answer3)
  If the mean of the distribution is 2.6, then the value of y is

  Variate x	1	2	3	4	5
  Frequency f of x	4	5	Y	1	2

  A)
  24         done clear
  B)
  13 done clear
  C)
  8          done clear
  D)
  3 done clear
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• question_answer4)
  Computer the medium form the following table

  Marks obtained	No. of students
  0-10	2
  10-20	18
  20-30	30
  30-40	45
  40-50	35
  50-60	20
  60-70	6
  70-80	3

  A)
  36.55    done clear
  B)
  35.55 done clear
  C)
  6.85                  done clear
  D)
  None of these done clear
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• question_answer5)
  The harmonic mean of 4, 8, 16 is
  A)
  6.4                    done clear
  B)
  6.7 done clear
  C)
  6.85                  done clear
  D)
  7.8 done clear
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• question_answer6)
  Following are the marks obtained by 9 students in a mathematics test: 50, 69, 20, 33, 39, 40, 65, 59 the mean deviation from the median is
  A)
  9                      done clear
  B)
  10.5 done clear
  C)
  12.67 done clear
  D)
  14.76 done clear
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• question_answer7)
  In a moderately skewed distribution, the values of mean and median are 5 and 6, respectively. The value of mode in such a situation is approximately equal to
  A)
  8                      done clear
  B)
  11 done clear
  C)
  6                      done clear
  D)
  None of these done clear
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• question_answer8)
  Runs scored by a batsman in 10 innings are: 38, 70, 48, 34, 42, 55, 63, 46, 54, 44 the mean deviation is
  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_answer9)
  If each observation of a raw data whose variance is \[\sigma \]of the new set is
  A)
  \[{{\sigma }^{2}}\]                   done clear
  B)
  \[{{h}^{2}}{{\sigma }^{2}}\] done clear
  C)
  \[h\,{{\sigma }^{2}}\]               done clear
  D)
  \[h+{{\sigma }^{2}}\] done clear
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• question_answer10)
  The following data give the distribution of heights of students:

  Height (in cm)	160	150	152	152	161	154	155
  Name of students	12	8	4	4	3	3	7

  The median of the distribution is
  A)
  154                   done clear
  B)
  155 done clear
  C)
  160       done clear
  D)
  161 done clear
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• question_answer11)
  The variance of the data 2, 4, 6, 8, 10 is
  A)
  6                      done clear
  B)
  7 done clear
  C)
  8                      done clear
  D)
  None of these done clear
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• question_answer12)
  The standard deviation of 25 number is 40. If each of the numbers in increased by 5, then the new standard deviation will be
  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_answer13)
  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)
  10 K done clear
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• question_answer14)
  Standard deviation for first 10 natural numbers is
  A)
  5.5                    done clear
  B)
  3.87 done clear
  C)
  2.97      done clear
  D)
  2.87 done clear
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• question_answer15)
  The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all the observations is
  A)
  50000   done clear
  B)
  250000 done clear
  C)
  252500  done clear
  D)
  255000 done clear
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• question_answer16)
  For\[\left( 2n+1 \right)\] observations \[{{x}_{1}},{}^{-}{{x}_{1}},\,\,{{x}_{2}},{}^{-}{{x}_{2}},\,\,...,\,\,{{x}_{n}},\,{{\,}^{-}}{{x}_{n}}\] and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?
  A)
  SD>MD done clear
  B)
  SD>MD done clear
  C)
  SD=MD done clear
  D)
  Nothing can be said in general about the relationship between SD and MD done clear
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• question_answer17)
  Let\[{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\]and\[{{x}_{5}}\]be the observations with mean m and standard deviation s. The standard deviation of the observations \[k{{x}_{1}},\]\[k{{x}_{2}},\]\[k{{x}_{3}},\]\[k{{x}_{4}},\]and \[k{{x}_{5}},\] is
  A)
  \[k+s\]   done clear
  B)
  s/k done clear
  C)
  ks         done clear
  D)
  s done clear
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• question_answer18)

  Consider the following statements:

  I. Mode can be computed from histogram.

  II. Median is not independent of change of scale.

  III. Variance is independent of change of origin and scale. Which of these is/ are correct?

  A)
  only I    done clear
  B)
  only II done clear
  C)
  only I and II       done clear
  D)
  I, II and III done clear
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• question_answer19)
  The median of a set of nine distinct observations is 20.5 if each of the largest four observations of the set is increased by 2, then the median of the new set
  A)
  is increased by 2. done clear
  B)
  is decreased by 2. done clear
  C)
  is two times the original median. done clear
  D)
  remains the same as that of the original set. done clear
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• question_answer20)
    In a series of 2n observation half of them equal a and remaining half equal \[-\,a\] if the standard deviation of the observations is 2, then \[\left| a \right|\] equals
  A)
  \[\frac{1}{n}\]               done clear
  B)
  \[\sqrt{2}\] done clear
  C)
  2                      done clear
  D)
  \[\frac{\sqrt{2}}{n}\] done clear
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• question_answer21)
  The standard deviation of some temperature data in \[{}^\circ C\] is 5. If the data were converted into\[{}^\circ F\], the new variance would be ______.
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• question_answer22)
  The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is _______.
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• question_answer23)
  Consider the first 10 positive integers. If we multiply each number by \[-\,1\] and then add 1 to each number, the variance of the numbers so obtained is _______.
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• question_answer24)
  In a class of 100 students, there are 70 boys average of whose marks I a subject is 75. If the average of marks of the complete class is 72, then the average of marks of the girls is _____.
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• question_answer25)
  In an experiment with 15 observations on x, the following results were available: \[\Sigma \,{{x}^{2}}=2830\], \[\Sigma \,x=170\] One observation, 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is _______.
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