JEE Main & Advanced Mathematics Statistics Question Bank

done Mean Total Questions - 32

• question_answer1)
  If the mean of 3, 4, x, 7, 10 is 6, then the value of x is
  A)
                  4              done clear
  B)
                  5 done clear
  C)
                  6              done clear
  D)
                  7 done clear
  View Solution play_arrow

• question_answer2)
  The mean of a set of numbers is \[\bar{x}\]. If each number is multiplied by l, then the mean of new set is
  A)
                  \[\bar{x}\]               done clear
  B)
                  \[\lambda +\bar{x}\] done clear
  C)
                  \[\lambda \bar{x}\]                done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer3)
  The mean of discrete observations \[{{y}_{1}},\,{{y}_{2}},\,......,\,{{y}_{n}}\] is given by [DCE 1999]
  A)
                  \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{n}\]       done clear
  B)
                  \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{\sum\limits_{i=1}^{n}{i}}\] done clear
  C)
                  \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}{{f}_{i}}}}{n}\]           done clear
  D)
                  \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}{{f}_{i}}}}{\sum\limits_{i=1}^{n}{{{f}_{i}}}}\] done clear
  View Solution play_arrow

• question_answer4)
  \[{{d}_{i}}\] is the deviation of a class mark \[{{y}_{i}}\] from ?a? the assumed mean and \[{{f}_{i}}\] is the frequency, if \[{{M}_{g}}=x+\frac{1}{\sum {{f}_{i}}}(\sum {{f}_{i}}{{d}_{i}})\], then x is
  A)
                  Lower limit             done clear
  B)
                  Assumed mean done clear
  C)
                  Number of observations         done clear
  D)
                  Class size done clear
  View Solution play_arrow

• question_answer5)
  The mean of a set of observation is \[\bar{x}\]. If each observation is divided by a, a ¹ 0 and then is increased by 10, then the mean of the new set is
  A)
                  \[\frac{{\bar{x}}}{\alpha }\]   done clear
  B)
                  \[\frac{\bar{x}+10}{\alpha }\] done clear
  C)
                  \[\frac{\bar{x}+10\alpha }{\alpha }\]    done clear
  D)
                  \[\alpha \bar{x}+10\] done clear
  View Solution play_arrow

• question_answer6)
  If the mean of the numbers \[27+x\], \[31+x\], \[89+x\], \[107+x,\,156+x\] is 82, then the mean of \[130+x,\,126+x,\,68+x,\,50+x,\,1+x\] is                [Pb. CET 1989; Kurukshetra CEE 2000; Kerala (Engg.) 2001]
  A)
                  75            done clear
  B)
                  157 done clear
  C)
                  82            done clear
  D)
                  80 done clear
  View Solution play_arrow

• question_answer7)
  Consider the frequency distribution of the given numbers

  Value :	1	2	3	4
  Frequency :	5	4	6	f

                  If the mean is known to be 3, then the value of f is
  A)
                  3              done clear
  B)
                  7 done clear
  C)
                  10            done clear
  D)
                  14 done clear
  View Solution play_arrow

• question_answer8)
  If the arithmetic mean of the numbers \[{{x}_{1}},{{x}_{2}},{{x}_{3}},\,......,\,{{x}_{n}}\] is \[\bar{x}\], then the arithmetic mean of numbers \[a{{x}_{1}}+b,\,a{{x}_{2}}+b,\,a{{x}_{3}}+b,\,........,a{{x}_{n}}+b\], where a, b are two constants would be
  A)
                  \[\bar{x}\]               done clear
  B)
                  \[n\,a\bar{x}+nb\] done clear
  C)
                  \[a\bar{x}\]             done clear
  D)
                  \[a\bar{x}+b\] done clear
  View Solution play_arrow

• question_answer9)
  The G.M. of the numbers \[3,\,{{3}^{2}},\,{{3}^{3}},\,......,\,{{3}^{n}}\] is                 [Pb. CET 1997]
  A)
                  \[{{3}^{2/n}}\]        done clear
  B)
                  \[{{3}^{(n-1)/2}}\] done clear
  C)
                  \[{{3}^{n/2}}\]        done clear
  D)
                  \[{{3}^{(n+1)/2}}\] done clear
  View Solution play_arrow

• question_answer10)
  The reciprocal of the mean of the reciprocals of n observations is their                                             [AMU 1985]
  A)
                  A.M.        done clear
  B)
                  G.M. done clear
  C)
                  H.M.        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer11)
  The harmonic mean of 3, 7, 8, 10, 14 is
  A)
                  \[\frac{3+7+8+10+14}{5}\]     done clear
  B)
                  \[\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{14}\] done clear
  C)
                  \[\frac{\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{14}}{4}\]        done clear
  D)
                  \[\frac{5}{\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{14}}\] done clear
  View Solution play_arrow

• question_answer12)
  If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is
  A)
                  30            done clear
  B)
                  30.1 done clear
  C)
                  29            done clear
  D)
                  31 done clear
  View Solution play_arrow

• question_answer13)
  The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is                   [Pb. CET 1989]
  A)
                  \[\frac{n+1}{2}\]     done clear
  B)
                  \[\frac{3n(n+1)}{2(2n+1)}\] done clear
  C)
                  \[\frac{(n+1)(2n+1)}{6}\]       done clear
  D)
                  \[\frac{n(n+1)}{2}\] done clear
  View Solution play_arrow

• question_answer14)
  If the values \[1,\,\frac{1}{2},\,\frac{1}{3},\,\frac{1}{4},\,\frac{1}{5},\,.....,\frac{1}{n}\] occur at frequencies 1, 2, 3, 4, 5, ?.,n in a distribution, then the mean is
  A)
                  1              done clear
  B)
                  n done clear
  C)
                  \[\frac{1}{n}\]         done clear
  D)
                  \[\frac{2}{n+1}\] done clear
  View Solution play_arrow

• question_answer15)
  The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is   [AMU 1992; DCE 1996]
  A)
                  \[\frac{1}{5}\]         done clear
  B)
                  \[\frac{15}{4}\] done clear
  C)
                  4              done clear
  D)
                  8 done clear
  View Solution play_arrow

• question_answer16)
  A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than                     
  A)
                  60%         done clear
  B)
                  65% done clear
  C)
                  80%         done clear
  D)
                  90% done clear
  View Solution play_arrow

• question_answer17)
  The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is
  A)
                  30            done clear
  B)
                  40 done clear
  C)
                  50            done clear
  D)
                  60 done clear
  View Solution play_arrow

• question_answer18)
  The A.M. of a 50 set of numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the A.M. of the remaining set of numbers is                [Kurukshetra CEE 1993]
  A)
                  38.5         done clear
  B)
                  37.5         done clear
  C)
                  36.5         done clear
  D)
                  36 done clear
  View Solution play_arrow

• question_answer19)
  An automobile driver travels from plane to a hill station 120 km distant at an average speed of 30 km per hour. He then makes the return trip at an average speed of 25 km per hour. He covers another 120 km distance on plane at an average speed of 50 km per hour. His average speed over the entire distance of 360 km will be
  A)
                  \[\frac{30+25+50}{3}\]km/hr done clear
  B)
                  \[{{(30,\,25,\,50)}^{\frac{1}{3}}}\] done clear
  C)
                  \[\frac{3}{\frac{1}{30}+\frac{1}{25}+\frac{1}{50}}\]km/hr   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer20)
  The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by \[\frac{1}{2}\]kg; the weight of the teacher is                 [Kerala (Engg.) 2002]
  A)
                  40.5 kg    done clear
  B)
                  50 kg       done clear
  C)
                  41 kg       done clear
  D)
                  58 kg done clear
  View Solution play_arrow

• question_answer21)
  If \[{{\bar{x}}_{1}}\] and \[{{\bar{x}}_{2}}\] are the means of two distributions such that \[{{\bar{x}}_{1}}<{{\bar{x}}_{2}}\] and \[\bar{x}\] is the mean of the combined distribution, then
  A)
                  \[\bar{x}<{{\bar{x}}_{1}}\]     done clear
  B)
                  \[\bar{x}>{{\bar{x}}_{2}}\] done clear
  C)
                  \[\bar{X}=\frac{{{{\bar{X}}}_{1}}+{{{\bar{X}}}_{2}}}{2}\]      done clear
  D)
                  \[{{\bar{x}}_{1}}<\bar{x}<{{\bar{x}}_{2}}\] done clear
  View Solution play_arrow

• question_answer22)
  The A.M. of n observations is M. If the sum of \[n-4\] observations is a, then the mean of remaining 4 observations is
  A)
                  \[\frac{n\,M-a}{4}\]               done clear
  B)
                  \[\frac{n\,M+a}{2}\] done clear
  C)
                  \[\frac{n\,M-A}{2}\]               done clear
  D)
                  n M + a done clear
  View Solution play_arrow

• question_answer23)
  If the mean of the distribution is 2.6, then the value of y is [Kurukshetra CEE 2001]

  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
  View Solution play_arrow

• question_answer24)
  In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls                                               [AIEEE 2002]
  A)
                  73            done clear
  B)
                  65            done clear
  C)
                  68            done clear
  D)
                  74 done clear
  View Solution play_arrow

• question_answer25)
  If the mean of the set of numbers \[{{x}_{1}},\,{{x}_{2}},\,{{x}_{3}},\,.....,\,{{x}_{n}}\] is \[\bar{x}\], then the mean of the numbers \[{{x}_{i}}+2i\], \[1\le i\le n\] is [Pb. CET 1988]
  A)
                  \[\bar{x}+2n\]       done clear
  B)
              \[\bar{x}+n+1\]  done clear
  C)
                  \[\bar{x}+2\]         done clear
  D)
                  \[\bar{x}+n\] done clear
  View Solution play_arrow

• question_answer26)
  The harmonic mean of 4, 8, 16 is                              [AMU 1995]
  A)
                  6.4          done clear
  B)
                  6.7          done clear
  C)
                  6.85        done clear
  D)
                  7.8 done clear
  View Solution play_arrow

• question_answer27)
  Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is       [Kurukshetra CEE 1994]
  A)
                  48           done clear
  B)
                  \[82\frac{1}{2}\]   done clear
  C)
              50           done clear
  D)
                  80 done clear
  View Solution play_arrow

• question_answer28)
  A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in chemistry test are 50, 60, 55 and 45 respectively for the four sections, the over all average of marks per students is    [Pb. CET 2000]
  A)
                  53           done clear
  B)
                  45 done clear
  C)
                  55.3        done clear
  D)
                  52. 25 done clear
  View Solution play_arrow

• question_answer29)
  The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is           [Pb. CET 2001]
  A)
                  18           done clear
  B)
                  25 done clear
  C)
              26           done clear
  D)
                  30 done clear
  View Solution play_arrow

• question_answer30)
  The mean weight per student in a group of seven students is 55 kg If the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weights of the seventh student is          [Pb. CET 2002]
  A)
                  55kg       done clear
  B)
                  60kg done clear
  C)
              57kg       done clear
  D)
                  50kg done clear
  View Solution play_arrow

• question_answer31)
  The class marks of a distribution are 6,10, 14, 18, 22, 26, 30 then the class size is                                            [Pb. CET 2004]
  A)
                  4              done clear
  B)
                  2 done clear
  C)
              5              done clear
  D)
                  8 done clear
  View Solution play_arrow

• question_answer32)
  Let \[{{x}_{1}},\,{{x}_{2}},....,{{x}_{n}}\] be n observations such that \[\sum x_{i}^{2}=400\] and \[\sum x_{i}^{{}}=80\]. Then a possible value of n among the following is          [AIEEE 2005]
  A)
                  9              done clear
  B)
                  12 done clear
  C)
                  15            done clear
  D)
                  18 done clear
  View Solution play_arrow