The mean of first n natural numbers is $\frac{5n}{9}.$ Find n.
(1) 5
(2) 4
(3) 9
(4) None of these
Mean of a certain number of observations is m. If each observation is divided by x (x ≠ 0) and increased by y, then the mean of new observations is
(1) mx + y
(2) $\frac{mx+y}{x}$
(3) $\frac{m+xy}{x}$
(4) m + xy
If the difference of mode and median of a data is 24, then the difference of median and mean is
(1) 12
(2) 24
(3) 8
(4) 36
The mode of the observations 2x + 3, 3x – 2, 4x + 3, x – 1, 3x – 1, 5x + 2 (x is a positive integer) can be
(1) 3
(2) 5
(3) 7
(4) 9
The median of 21 observations is 18. If two observations 15 and 24 are included to the observations, then the median of the new series is
(1) 15
(2) 18
(3) 24
(4) 16
If the quartile deviation of a set of observations is 10 and the third quartile is 35, then the first quartile is
(1) 24
(2) 30
(3) 17
(4) 15
The upper class limit of inclusive type class interval 10–20 is ______.
(1) 10.5
(2) 20
(3) 20.5
(4) 17.5
The semiinter quartile range of the observations 9, 12, 14, 6, 23, 36, 20, 7, 42 and 32 is
(1) 12.75
(2) 12.5
(3) 9.75
(4) 9.5
Find the mode of the following discrete series.
x 
f 
x 
f 
1 
5 
6 
8 
3 
7 
12 
6 
5 
3 
15 
5 
(1) 3
(2) 12
(3) 8
(4) 6
The mean deviation of a^{3} + b^{3} and a^{3} – b^{3} (where a and b > 0) is _________.
(1) a^{3}
(2) b^{3}
(3) 2a^{3}
(4) 2b^{3}
If the arithmetic mean of the observation x_{1}, x_{2}, x_{3}, ... x_{n}, is 1, then the arithmetic mean of $\frac{{x}_{1}}{k},\frac{{x}_{2}}{k},\frac{{x}_{3}}{k},\mathrm{...},\frac{{x}_{n}}{k}(k0)$ is
(1) greater than 1.
(2) less than 1.
(3) equal to 1.
(4) None of these
Range of 14, 12, 17, 18, 16 and x is 20. Find x (x > 0).
(1) 2
(2) 28
(3) 32
(4) Cannot be determined
The mean of a set of observation is a. If each observation is multiplied by b and each product is decreased by c. then the mean of new set of observations is ______.
(1) $\frac{a}{b}+c$
(2) ab – c
(3) $\frac{a}{b}c$
(4) ab + c
The mean deviation of first 8 composite numbers is _________.
(1) 2.9375
(2) 4.83
(3) 5.315
(4) 3.5625
Find the mode of the following discrete series.
x 
f 
x 
f 
1 
5 
5 
12 
2 
4 
6 
3 
3 
6 
7 
9 
4 
8 
8 
10 
(1) 4
(2) 8
(3) 5
(4) 7
The the highest score of certain data exceeds its lowest score by 16 and coefficient of range is $\frac{1}{3}.$ Find the sum of the highest score and the lowest score.
(1) 36
(2) 48
(3) 24
(4) 18
Find the mean deviation (approximately) about the mode for the following ungrouped data: 20, 25, 30, 18, 15, 40.
(1) 6.71
(2) 4.52
(3) 7.61
(4) 5.33
The mean of first n odd natural numbers is $\frac{{n}^{2}}{81}.$ Find n.
(1) 9
(2) 81
(3) 27
(4) None of these
The arithmetic mean of 12 observations is 15. If two observations 20 and 25 are removed then the arithmetic mean of remaining observations is
(1) 14.5
(2) 13.5
(3) 12.5
(4) 13
The arithmetic mean and mode of a data is 24 and 12 respectively, then the median of the data is _______.
(1) 20
(2) 18
(3) 20
(4) 22
The interquartile range of the observations 3, 5, 9, 11, 13, 18, 23, 25, 32 and 39 is
(1) 24
(2) 17
(3) 31
(4) 8
Find the mean deviation from die mode for the following ungrouped data: 2.5, 6.5, 7.3, 12.3, 16.2.
(1) 4.34
(2) 5.57
(3) 2.33
(4) 6.72
The mean of the following distribution is 5, then find the value of b.
x 
f 
3 
2 
5 
a 
7 
5 
4 
b 
(1) 10
(2) 6
(3) 8
(4) None of these
The mean deviation of $\frac{a+b}{2}$ and $\frac{ab}{2}$ (where a and b > 0) is ________.
(1) $\frac{b}{2}$
(2) $\frac{a}{2}$
(3) a
(4) b
If the mean of x + 2, 2x + 3, 3x + 4 and 4x + 5 is x + 2, then find the value of x.
(1) 0
(2) 1
(3) –1
(4) 2
The range of 15, 14, x, 25, 30, 35 is 23. Find the least possible value of x.
(1) 14
(2) 12
(3) 13
(4) 11
Find the median of the following data.
Class Interval 
f 
0–10 
12 
10–20 
13 
20–30 
25 
30–40 
20 
40–50 
10 
(1) 25
(2) 23
(3) 24
(4) 26
In the following table, pass percentage of three schools from the year 2001 to the year 2006 are given. Which school students' performance is more consistent?

2001 
2002 
2003 
2004 
2005 
2006 
School X 
80 
89 
79 
83 
84 
65 
School Y 
92 
94 
76 
75 
80 
63 
School Z 
93 
97 
67 
63 
70 
85 
(1) X
(2) Y
(3) Z
(4) X and Y
The median of the following discrete series is
x 
f 
3 
5 
6 
2 
5 
4 
8 
6 
12 
7 
7 
6 
(1) 7
(2) 8
(3) 9
(4) 6
Which of the following does not change for the observations 23, 50, 27, 2x, 48, 59, 72, 89, 5x, 100, 120, when x lies between 15 and 20?
(1) Arithmetic mean
(2) Range
(3) Median
(4) Quartile deviation
If the ratio of mean and median of a certain data is 2 : 3, then find the ratio of its mode and mean.
(1) 4 : 3
(2) 7 : 6
(3) 7 : 8
(4) 5 : 2
If mean of the following distribution is 13, then the value of p is
x 
5 
10 
12 
17 
16 
20 
f 
9 
3 
p 
8 
7 
5 
(1) 6
(2) 7
(3) 10
(4) 4
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
(1) 8 : 9
(2) 9 : 10
(3) 9 : 7
(4) 8 : 11
If the arithmetic mean of the following distribution is 8.2, then find the value of p.
x 
1 
3 
5 
9 
11 
13 
f 
3 
2 
7 
p 
4 
8 
(1) 5
(2) 6
(3) 9
(4) None of these
The median of the series 8, 12,15, 7, x, 19 and 22 lies in the interval.
(1) [12, 15]
(2) [7, 15]
(3) [15, 17]
(4) [9. 12]
The mode of the following distribution is
Class Interval 
f 
1–5 
4 
6–10 
7 
11–15 
10 
16–20 
8 
21–25 
6 
(1) 14.5
(2) 16.5
(3) 10.5
(4) 13.5
The mean of the following data is
Class Interval 
f 
10–15 
5 
15–20 
7 
20–25 
3 
25–30 
4 
30–35 
8 
(1) 22
(2) 23.05
(3) 24.05
(4) 27.05
The median of the following frequency distribution is
Class Interval 
f 
0–10 
5 
10–20 
8 
20–30 
7 
30–40 
10 
40–50 
20 
(1) 35
(2) 30
(3) 40
(4) 45
Find the quartile deviation of the following discrete series.
x 
7 
5 
4 
8 
12 
10 
f 
2 
4 
6 
10 
9 
7 
(1) 6.5
(2) 4.5
(3) 3.5
(4) 2.5
The given figure represents the percentage of marks on Xaxis and the number of students on Yaxis.
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 Xaxis and the number of students on Yaxis.
Find the number of students who scored greater than or equal to 90% of marks.
(1) 47
(2) 45
(3) 5
(4) 10
In a class of 15 students, on an average, each student got 12 books. If exactly two students received same number of books, and the average of books received by remaining students be an integer, then which of the following could be the number of books received by each of the two students who received same number of books?
(1) 11
(2) 15
(3) 20
(4) 25
Find the quartile deviation of the following discrete series.
x 
3 
5 
6 
8 
10 
12 
f 
7 
2 
3 
4 
5 
6 
(1) 4
(2) 3
(3) 3.5
(4) 4.5
Weight (in kg) 
Number of Students 
20 
8 
22 
4 
24 
3 
25 
7 
30 
5 
Find the mean deviation (approximately) about the median for the above data.
(1) 2.5
(2) 1.5
(3) 3
(4) 0.5
Find the mean deviation (approximately) about the mean for the following.
Class Interval 
f 
0–5 
3 
5–0 
4 
10–15 
8 
15–20 
10 
20–25 
5 
(1) 5
(2) 4
(3) 6
(4) 3
If the average mark of 15 students is 60 and the average mark of another 10 students is 70, then find the average mark of 25 students.
The following are the steps involved in solving the above problem. Arrange them in sequential order.
(A) Average marks of 25 students $\text{=}\frac{1600}{25}=64$
(B) The total marks of 15 students = 15 × 60 = 900
The total marks of 10 students = 10 × 70 = 700
(C) The total marks of 25 students = 900 + 700 = 1600
(1) BCA
(2) BAC
(3) CBA
(4) CAB
In a class of 25 boys and 20 girls, the mean weight of the boys is 40 kg and the mean weight of the girls is 35 kg. Find the mean weight of the class.
The following are the steps involved in solving the above problem. Arrange them in sequential order.
(A) The total weight of 25 boys = 25 × 40 = 1000 kg
The total weight of 20 girls = 20 × 35 = 700 kg
(B) The mean weight of the class $=\frac{\text{1700}}{\text{45}}=\text{37}\frac{\text{7}}{\text{9}}\text{kg}$
(C) The total weight of 45 students = 1000 kg + 700 kg 1700 kg
(1) ABC
(2) ACB
(3) BCA
(4) CBA
If p < q < 2p; the median and mean of p, q and 2p are 36 and 31 respectively, then find the mean of p and q.
(1) 21.5
(2) 23
(3) 27.5
(4) 24
If x < y < 2x; the median and the mean of x, y and 2x are 27 and 33 respectively, then find the mean of x and y.
(1) 23.5
(2) 24
(3) 23
(4) 25.5
The mean of a set of 12 observations is 10 and another set of 8 observations is 12. The mean of combined set is ________.
(1) 11
(2) 10.8
(3) 11.2
(4) 0.6
A class of 40 students is divided into four groups named as A, B, C and D. Groupwise percentage of marks scored by them are given below in the table.
A 
B 
C 
D 
20 
42 
10 
21 
30 
51 
25 
69 
40 
45 
85 
70 
25 
58 
73 
86 
22 
53 
98 
53 
45 
64 
43 
68 
65 
72 
64 
99 
By using the coefficient of range find which of the group has shown good performance.
(1) A
(2) B
(3) C
(4) D
Life (in hour) of 10 bulbs from each of four different companies A, B, C and D are given below in the table.
A 
B 
C 
D 
120 
700 
950 
530 
1600 
502 
330 
650 
280 
1430 
1200 
720 
420 
625 
500 
550 
800 
780 
445 
748 
770 
335 
1260 
570 
270 
224 
375 
635 
455 
1124 
1130 
804 
150 
473 
185 
500 
By using the coefficient of range find which company has shown the best consistency in its quality?
(1) A
(2) B
(3) C
(4) D
If the mode of the observations 5, 4, 4, 3, 5, x, 3, 4, 3, 5, 4, 3 and 5 is 3, then find the median of the observations.
(1) 3
(2) 4
(3) 5
(4) 3.5
In a colony, the average age of the boys is 14 years and the average age of the girls is 17 years. If the average age of the children in the colony is 15 years, find the ratio of number of boys to that of girls,
(1) 1 : 2
(2) 2 : 1
(3) 2 : 3
(4) 3 : 2
Find the median of the following data.
Class Interval 
f 
0–4 
3 
4–8 
6 
8–12 
6 
12–16 
6 
16–20 
8 
(1) 13
(2) 12
(3) 11
(4) 10
In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each. Remaining students brought atleast one book each and no two students brought the same number of books. If the average number of books brought in the class is a positive integer, then what could be the total number of books brought by the remaining students?
(1) 12
(2) 16
(3) 14
(4) 8
The mean of a set of 20 observations is 8 and another set of 30 observations is 10. The mean of combined set is __________.
(1) 9.2
(2) 10.8
(3) 11.2
(4) 9.8
Find the approximate value of mean deviation about the mode of the following data.
Class Interval 
f 
0–10 
4 
10–20 
6 
20–30 
3 
30–40 
9 
40–50 
5 
(1) 11.5
(2) 12.5
(3) 13.5
(4) 14.5
The mean of the following distribution is 4. Find the value of q.
x 
2 
3 
4 
5 
7 
f 
4 
4 
2 
3 
q 
(1) 2
(2) 3
(3) 0
(4) 4
If the ratio of mean and median of a certain data is 5 : 7, then find the ratio of its mode and mean.
(1) 2 : 5
(2) 11 : 5
(3) 6 : 5
(4) 2 : 3
Find the mode of the following discrete series.
x 
1 
2 
3 
4 
5 
6 
7 
8 
9 
f 
3 
8 
15 
1 
9 
12 
14 
5 
7 
(1) 7
(2) 5
(3) 2
(4) 3
Find the median of the following data.
x 
12 
15 
18 
21 
24 
f 
4 
7 
2 
3 
4 
(1) 12
(2) 16
(3) 18
(4) 15
Find the mean deviation about the median for the following data.
x 
1 
2 
3 
4 
5 
6 
f 
3 
7 
5 
8 
2 
5 
(1) 1
(2) $0.\overline{7}$
(3) 3
(4) $1.\overline{3}$
Find the mode for the following data.
Class Interval 
f 
0–9 
2 
10–19 
4 
20–29 
7 
30–39 
5 
40–49 
3 
(1) 30
(2) 25.5
(3) 32
(4) 33
Find the quartile deviation of the following discrete series.
x 
8 
10 
13 
16 
19 
22 
f 
4 
7 
8 
3 
5 
4 
(1) 3.5
(2) 6
(3) 5
(4) 4.5
Find the arithmetic mean of the observations x + 5, x + 6, x + 10, x + 11, x + 14, x + 20 (where x is any real number).
(1) x + 11
(2) x + 5
(3) x + 13
(4) x + 7
Find the mode of the following discrete series.
x 
1 
2 
3 
4 
5 
6 
7 
8 
9 
f 
3 
8 
15 
1 
9 
12 
17 
5 
7 
(1) 7
(2) 5
(3) 2
(4) 3
Find the mean of the following continuous distribution.
Class Interval 
f 
0–10 
8 
10–20 
4 
20–30 
6 
30–40 
3 
40–50 
4 
(1) 20.8
(2) 21.4
(3) 21.8
(4) 22.2
Which of the following is not changed for the observations 31, 48, 50, 60, 25, 8, 3x, 26, 32?
(where x lies between 10 and 15).
(1) Arithmetic mean
(2) Range
(3) Median
(4) Quartile deviation
Ravi travelled from P to Q at 12 kmph. He then travelled from Q to R at 32 kmph and then from R to S at 10.8 kmph. 2PQ = 3QR = 4RS. Find Ravi’s average speed for his entire journey. (in kmph)
(1) $\frac{64}{5}$
(2) $\frac{72}{5}$
(3) $\frac{54}{5}$
(4) $\frac{66}{5}$