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If the arithmetic mean of the first n natural numbers is 15, then n is_____________________
(1) 15
(2) 30
(3) 14
(4) 29

If the arithmetic mean of 7, 8, x, 11, 14 is x, then x is________________
(1) 9
(2) 9.5
(3) 10
(4) 29

Find the mode of the data 5, 3, 4, 3, 5, 3, 6, 4, 5.
(1) 5
(2) 4
(3) 3
(4) Both (1) and (2)

The median of the data 5, 6, 7, 8, 9,  10 is _______________
(1) 7
(2) 8
(3) 7.5
(4) 8.5

If a mode exceeds a mean by 12, then the mode exceeds the median by ________________
(1) 4
(2) 8
(3) 6
(4) 10

If the less that cumulative frequency of a class is 50 and that of the previous class is 30, then the frquency of that class is ______________
(1) 10
(2) 20
(3) 40
(4) 30

 $$\begin{gathered} If the median of the data, x_1, x_2,x_3,x_4,x_5,x_6,x_7,x_8 is a, then find the median of the data x_3,x_4,x_5,x_{6,} \\ (where x_1<x_2<x_3<x_4<x_5<x_6<x_7<x_8) \end{gathered}$$
(1) a
(2) $\frac{a}{2}$
(3) $\frac{a}{4}$
(4) $\frac{a}{3}$

The mode of the data 6, 4, 3, 6, 4,3, 4, 6, 5 and x can be :
(1) Only 5
(2) Both 4 and 6
(3) Both 3 and 6
(4) 3, 4 or 6

If the greater than cumulative frequency of a class is 60 and that of the next class is 40, then find the frequency of that class.
(1) 10
(2) 20
(3) 50
(4) 30

If the difference between the mode and median is 2, then the difference between the median and mean is _________(in the given order)
(1) 2
(2) 4
(3) 1
(4) 0

In a series of observations, SD is 7 and mean in 28.  Find the coefficient of variation.
(1) 4
(2) $\frac{1}{4}$
(3) 25
(4) 12.5

$If the SD of x_1, x_2,x_3,......,x_{n }is 5, then find SD of x_1+5, x_2+5, x_3+5,.....x_n+5.$
(1) 0
(2) 10
(3) 5
(4) 2

In a series of observations coefficient of variation is 16 and mean is 25.  Find the variace.
(1) 4
(2) 8
(3) 12
(4) 16

$If the SD of y_1,y_2,y_3,.....y_{n is 6, then variance of (y_1-3),{(y}_{}}$₂-3),(y3-3),......,(yn-3) is ______________________________
(1) 6
(2) 36
(3) 3
(4) 27

Lower quartile, upper quartile and interquartile range are $Q_1, Q_2 and Q$.  If the average of $Q, Q_1 and Q_3$ is 40 and semi-interquartile range is 6, then find the lower quartile.
(1) 24
(2) 36
(3) 48
(4) 60
 

  The weight of 20 students in a class are give below.
$\begin{array}{cc}Weight (in kg) & Number of students\\ 31& 6\\ 32& 3\\ 33& 5\\ 34& 2\\ 35& 4\end{array}$
Find  the median of the above frquency distribution.
(1) 32.5
(2) 33
(3) 33.5
(4) 32

The weight of 20 students in a class are give below.
$\begin{array}{cc}Weight (in kg) & Number of students\\ 31& 6\\ 32& 3\\ 33& 5\\ 34& 2\\ 35& 4\end{array}$
The interquartile range of the above frequecy distribution is _____________
(1) 4
(2) 3
(3) 2
(4) 1

If the average of a, b, c and d is the average of b and c, then which of the following  is necessary true?
(1) (a+d) = (b+c)
(2) (a+b) = (c+d)
(3) (a-d) = (b-c)
(4) $\frac{(a+b)}{4}=\frac{(b+c)}{2}$

Find the interquartile range of the data 3, 6, 5, 4, 2, 1 and 7.
(1) 4
(2) 3
(3) 2
(4) 1

If the mean of the lower quartile and upper quartile is 10 and the semi-interquartile range is 5, then the lower quartile and the upper quartile are __________ and _________.
(1) 2, 12
(2) 3, 13
(3) 4, 14
(4) 5, 15

The lower quartile of the data 5, 3, 4, 6, 7, 11, 9 is ___________
(1) 4
(2) 3
(3) 5
(4) 6

Find the arithmetic mean of the first 567 natural numbers.
(1) 284
(2) 283.5
(3) 283
(4) 285

If a < b < c < d < and a, b, c ,d are non-zero integers, the mean and median of a, b, c, d is 0 then which of the following is correct ?
(1) b = - c
(2) a = - a
(3) Both (1) and (2)
(4) None of these

The mean of 16 observation is 16.  If one observation 16 is deleted and three observation 5, 5 and 6 are inculed, then find the mean of the final observations.
(1) 16
(2) 15.5
(3) 13.5
(4) None of these

$If L=44.5, N=50, F=15, f=5 and C=20, then find the median from of given data.$
(1) 84.5
(2) 74.5
(3) 64.5
(4) 54.5

$If L=39.5, {∆}_1=6, {∆}_2=9 and c=10, then find the mode of the data.$
(1) 45.5
(2) 43.5
(3) 46.5
(4) 44.5

The average weight of 55 students is 55 kg, and the average weight of another 45 students is 45 kg.  Find the average weight of all the students.
(1) 48 kg
(2) 50 kg
(3) 50.5 kg
(4) 52.25 kg

If the mean of 26, 19, 15, 24, and x is x, then find the median of the data.
(1) 23
(2) 22
(3) 20
(4) 21

The mean and median of the data a, b and c are 50 and 35, where a < b < c.  If c - a = 55, then find (b - a).
(1) 8
(2) 7
(3) 3
(4) 5

If a < b < 2a, and the mean and the median of a, b and 2a are 15 and 12, then find a.
(1) 7
(2) 11
(3) 10
(4) 8

The variance of $6x_i+3$ is 30, find the standard deviation of $x_i$.
(i) $\frac{5}{\sqrt{6}}$
(2) $\sqrt{\frac{5}{6}}$
(3) 30
(4) $\sqrt{30}$

The frequency distribution of the marks obtained by 28 students in a test carrying 40 marks is given below :
$\begin{array}{cc}Marks & Number of students\\ 0-10& 6\\ 10-20& x\\ 20-30& y\\ 30-40& 6\end{array}$
If the mean of the above data is 20, then find the difference between x and y.
(1) 3
(2) 2
(3) 1
(4) 0

The given figure represents the percentage of marks on the X-axis and the number of students on Y-axis.

Find the number of students who scored less than or equal to 50% of marks.
(1) 35
(2) 15
(3) 20
(4) 30

The given figure represents the percentage of marks on the X-axis and the number of students on Y-axis.

Find the number of students who scored greater than or equal to 90 % of marks.
(1) 47
(2) 45
(3) 5
(4) 10

Find the variance of the scores 2, 4, 6, 8, and 10.
(1) 2
(2) 4
(3) 6
(4) 8

If A = 55.5, N = 100, C = 20, and $\sum _{}{f}_i{d}_i =60, then find the mean from the given data.$
(1) 67.5
(2) 57.5
(3) 77.5
(4) 47.5

Mode for the following distribution is 17.5 and x is less than 6. Find x.
$\begin{array}{cc}Class Interval & Frequency\\ 0-5& 5\\ 5-10& 2\\ 10-15& 3\\ 15-20& 6\\ 20-15& x\end{array}$
(1) 3
(2) 2
(3) 4
(4) 5

Find the coefficient of variation for the given distribution.
$\begin{array}{cc}Class Interval & Frequency\\ 0-6& 2\\ 6-12& 4\\ 12-18& 6\end{array}$
(1) $\frac{\sqrt[200]{6}}{11}$
(2) $\frac{\sqrt[200]{3}}{11}$
(3) $\frac{500}{11}$
(4) $\frac{\sqrt[200]{5}}{11}$

Find the variance for the given distribution :
$\begin{array}{cc}Class Interval & Frequency\\ 0-6& 2\\ 6-12& 4\\ 12-18& 6\end{array}$
(1) 24
(2) 12
(3) 20
(4) 25

Find the mean of the quartiles $Q_1,Q_2 and Q_3$ of the data 5, 9, 8, 12, 7, 13, 10, 14.
(1) 9
(2) 10
(3) 9.5
(4) 11.5

Which of the following cannot be determined?
(A) Range of the factors of 64
(B) Range of the first 10 positive integers
(1) A
(2) B
(3) Both (A) and (B)
(4) None of these

Find the mean of the following data.
Range of first n natural numbers, range of negative integers from -n to -1 (where -n < -1), range of first n positive even integers and range of first n positive odd integers.
(1) $\frac{3}{2}\left(n-1\right)$
(2) $\frac{3n-2}{2}$
(3) $\frac{3}{2}\left(n-2\right)$
(4) $\frac{4n-3}{2}$

The following are the steps involved in finding the mean of the data.
$\begin{array}{cc} x & f\\ 10& 1\\ 8& 3\\ 6& 5\\ 4& 7\\ 2& 9\end{array}$
Arrange them in sequential order.
 $$\begin{gathered} \left(A\right) \therefore Mean=\frac{\sum _{}fx}{\sum _{}f}=\frac{110}{25} \\ \left(B\right) \sum _{}fx=10+24+30+28+18 \\ \sum _{}f=1+3+5+7+9 \\ \left(C\right) \therefore Mean=4, 4 \\ \left(D\right) \sum _{}fx=110 and \sum _{}f=25 \end{gathered}$$
(1) ABDC
(2) ACBD
(3) BDAC
(4) BCAD

The mean weight of a group of 9 students is 19 kg.  If a boy of weight 29 kg is joined in the group, then find the mean weight of 10 students.
The following are the steps involved in solving the above problem.  Arrange them in sequential order.
$$\begin{gathered} \left(A\right) The mean weight of 10 students=\frac{200}{10} kg \\ \left(B\right) The total weight of 9 students=9\times 19 kg =171 kg \\ \left(C\right) The total weight of 10 students=(171+29) kg = 200 kg \\ \left(D\right) \therefore The mean weight = 20 kg \end{gathered}$$
(1) BCAD
(2) BDAC
(3) BDCA
(4) BCDA

The arithmetic mean of the following data is 7.  Find (a+b).
$\begin{array}{cc} x & f\\ 4& a\\ 6& 4\\ 7& b\\ 9& 5\end{array}$
(1) 4
(2) 2
(3) 3
(4) Cannot be determined

The performance of four students in annual report is given below.
$\begin{array}{ccc}Name of student& Mean score \left(\overline{x}\right) & SD \left(\sigma \right)\\ Dheeraj& 75& 11.25\\ Nishitha& 65& 5.98\\ Sindhuja& 48& 8.88\\ Akshitha& 44& 5.28\end{array}$
Who is more consistent than the others ?
(1) Dheeraj
(2) Nishitha
(3) Sindhuja
(4) Akshitha

The performance of four students in annual report is given below.
$\begin{array}{ccc}Name of student& Mean score \left(\overline{x}\right) & SD \left(\sigma \right)\\ Dheeraj& 75& 11.25\\ Nishitha& 65& 5.98\\ Sindhuja& 48& 8.88\\ Akshitha& 44& 5.28\end{array}$
Who is less consistent than the others ?
(1) Dheeraja
(2) Nishitha
(3) Sindhuja
(4) Akshitha

If the mean of the squares of first n natural numbers is 105, then find the median of the first n natural numbers.
(1) 8
(2) 9
(3) 10
(4) 11

Range of scores 18, 13, 14, 42, 22, 26 and x is 44 (x > 0).  Find the sum of the digits of x.
(1) 16
(2) 14
(3) 12
(4) 18

Find the arithmetic mean of the series 1, 3, 5,................, (2n - 1).
(1) $\frac{2n-1}{n}$
(2) $\frac{2n+1}{n}$
(3) n
(4) n+2

The arithmetic mean of the squares of first n natural numbers is _________
(1) $\frac{(n+1)(2n+1)}{6}$
(2) $\frac{n+1}{6}$
(3) $\frac{n^2-1}{6}$
(4) $\frac{n-1}{6}$

If X, M, Z are denoting mean, median and mode of a data and X : M = 9 : 8, then find the ratio M : Z
(1) 8 : 9
(2) 4 : 3
(3) 7 : 6
(4) 5 : 4

The arithmetic mean of the series $1, 3, 3^2,.....3^{n-1} is \_\_\_\_\_\_\_\_\_\_\_\_$
(1) $\frac{3^n}{2n}$
(2) $\frac{3^n-1}{2n}$
(3) $\frac{3^{n-1}}{n+1}$
(4) $\frac{3^n+1}{2n}$

The mean of the data x, x+a, x+2a, x+3a,......., (2n+1) terms is__________________
(1) x+(n-1)a
(2) x+(n+1)a
(3) x+(n+2)a
(4) x+an

The mean height of 25 boys in a class is 150 cm, and the mean height of 35 girls in the same class is 145 cm.  The combined mean height of 60 students in the class is____________(approximately).
(1) 143 cm
(2) 146 cm
(3) 147 cm
(4) 145 cm

The sum of 15 observations of a data is (434+x).  If the mean of the data is x, then find x.
(1) 25
(2) 27
(3) 31
(4) 33

The mean weight of 9 students is 25 kg.  If one more student is joined in the group the mean is unaltered, then the weight of the 10th student is ____________(in kg)
(1) 25
(2) 24
(3) 26
(4) 23

Observations of some data are $$\begin{gathered} \frac{x}{5}, x, \frac{x}{3}, \frac{2x}{3}, \frac{x}{4}, \frac{2x}{5} and \frac{3x}{4 } where x >0. If the median of the data is 4, then find the \\ value of \text{'}x\text{'}. \end{gathered}$$
(1) 5
(2) 7
(3) 8
(4) 10