CBSE Class 10 Mathematics Statistics MCQs Set 07

Question. Find the weighted mean of first 'n' natural numbers, whose weights are proportional to the corresponding numbers.
(a) \( \frac{2n+1}{3} \)
(b) \( \frac{n+1}{2} \)
(c) \( \frac{n(n+1)}{2} \)
(d) \( \frac{(n+1)(2n+1)}{6} \)
Answer: A

Question. What is the mean of -8, -4, 4 and 8?
(a) 1
(b) Zero
(c) 8
(d) 2
Answer: B

Question. Find the mean of the first six multiples of 3.
(a) 63
(b) 11.5
(c) 10.5
(d) 60
Answer: C

Question. The A.M. of a set of 50 numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, find the mean of the remaining observations.
(a) 36
(b) 37.5
(c) 36.5
(d) 38.5
Answer: B

Question. Find the mean of the first six prime numbers.
(a) 68.3
(b) 6.71
(c) 7
(d) 6.83
Answer: D

Question. The A.M. of 'n' numbers of a series is \( \bar{X} \). If the sum of first (n - 1) terms is 'k'. what is the \( n^{th} \) number?
(a) \( n\bar{X} - nk \)
(b) \( n\bar{X} - k \)
(c) \( \bar{X} - nk \)
(d) \( \bar{X} - k \)
Answer: B

Question. The mean age of a combined group of men and women is 25 years. If the mean age of the group of men is 26 years and that of the group of women is 21 years, find the percentage of men and women respectively in the group.
(a) 70, 30
(b) 30, 70
(c) 80, 20
(d) 60, 40
Answer: C

Question. The mean of 8 numbers is 25. If 5 is subtracted from each number, what will the new mean be?
(a) 20
(b) 15
(c) 160
(d) 2
Answer: A

Question. If the mean of first 'n' odd natural numbers is 'n' itself, what is the value of 'n'?
(a) 2
(b) 3
(c) 1
(d) Any natural number
Answer: D

Question. If the mean of 'n' observations, \( 1^2, 2^2, 3^2, \dots, n^2 \) is \( \frac{46n}{11} \), find the value of 'n'.
(a) 22
(b) 23
(c) 12
(d) 11
Answer: D

Question. The A.M. of 'n' observations is M. If the sum of (n-4) observations is 'a', what is the mean of remaining 4 observations?
(a) \( nM + a \)
(b) \( \frac{nM - a}{2} \)
(c) \( \frac{nM + a}{2} \)
(d) \( \frac{nM - a}{4} \)
Answer: D

Question. Identify the mode of the given distribution.
Marks:                ​​​​​​​     ​​​​​​​     ​​​​​​​4,     5,      6,      7,      8
Number of Students: 3,      5,      10,    6,      1
(a) 7
(b) 1
(c) 8
(d) 6
Answer: DFV

Question. Marks obtained by 12 students in a test are 37, 23, 16, 19, 34, 23, 5, 27, 36, 23, 20 and 38. Find the modal marks.
(a) 27
(b) 37
(c) 23
(d) 5
Answer: C

Question. If 10, 13, 15, 18, (x+1), (x+3), 30, 32, 35 and 41 are ten observations in the ascending order with median 24, find the value of 'x'.
(a) 42
(b) 22
(c) 10
(d) 32
Answer: B

Question. The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers is 20. Find the excluded number.
(a) 138
(b) 100
(c) 20
(d) 38
Answer: D

Question. If \( \bar{x} \) is the mean of \( x_1, x_2, \dots, x_n \), find the mean of \( (x_1 + 2a), (x_2 + 2a), (x_3 + 2a), \dots, (x_n + 2a) \).
(a) \( \bar{x} + 2a \)
(b) \( \bar{x} - 2a \)
(c) \( \frac{\bar{x}}{2} + 2a \)
(d) \( \frac{\bar{x}}{2} + a \)
Answer: A

Question. The mean weight of seven boys is 56 kg. Individual weights of six boys (in kg) are 52, 57, 55, 60, 59 and 55 respectively. Find the weight of the seventh boy.
(a) 52 kg
(b) 54 kg
(c) 57 kg
(d) 59 kg
Answer: B

Question. The mean of 150 items was found to be 60. Later on, it was discovered that the values of two items were taken as 52 and 8 instead of 152 and 88 respectively. Find the correct mean.
(a) 6.15
(b) 60.7
(c) 61.2
(d) 6.72
Answer: C

Question. Given that \( \bar{x} \) is the mean of \( x_1, x_2, \dots, x_n \), find the mean of \( \frac{x_1}{a}, \frac{x_2}{a}, \dots, \frac{x_n}{a} \).
(a) \( \bar{x} - a \)
(b) \( \bar{x} \)
(c) \( a\bar{x} \)
(d) \( \frac{\bar{x}}{a} \)
Answer: D

Question. In the frequency distribution, discrete data is given.
Variable (x):          0,       1,      2,      3,      4,      5
Frequency (f):      ​​​​​​​x,      20,     40,   40,     20,    4
If the mean is 2.5, what is the value of frequency 'x'?
(a) 0
(b) 1
(c) 3
(d) 4
Answer: D

Question. If \( x_1, x_2, \dots, x_n \) are 'n' observations such that \( \sum_{i=1}^n (x_i + 3) = 120 \) and \( \sum_{i=1}^n (x_i + 5) = 160 \), find 'n'.
(a) 40
(b) 20
(c) 60
(d) 70
Answer: B

Question. The arithmetic mean of the scores of a group of students in a test was 52%. The brightest 20% of them secured a mean score of 80 and the dullest 25%, a mean score of 31%. Which of the following is the mean score of the remaining 55%?
(a) 45%
(b) 50%
(c) 51.4% (approx)
(d) 54.6% (approx)
Answer: C

Question. The mean of 10 numbers is 7. If each number is multiplied by 12, find the mean of new set of numbers.
(a) 82
(b) 48
(c) 78
(d) 84
Answer: D

Question. The mean of the marks in Statistics of 100 students in class X was 72. The mean of marks for boys was 75, while their number was 70. What is the mean of marks of girls in the class?
(a) 35
(b) 65
(c) 68
(d) 86
Answer: B

Question. The given data are the times (in minutes), it takes seven students to go to school from their homes.
11, 6, 22, 7, 10, 6, 15
Which statement about the data is false?
(a) Their median is 11.
(b) Their mean is 11.
(c) Their range is 16.
(d) Their mode is 6.
Answer: A

Question. From a series of 50 observations, an observation 45 is dropped, but the mean remains the same. What was the mean of 50 observations?
(a) 50
(b) 49
(c) 45
(d) 40
Answer: C

Question. A person made 165 telephone calls in the month of May in a year. It was Friday on 1st May of the year. The average of telephone calls on Sundays of the month was 7. What was the average of the telephone calls per day on the rest of the days of the month?
(a) \( \frac{165}{31} \)
(b) 5
(c) 7
(d) \( \frac{137}{27} \)
Answer: B

Question. The numbers 4 and 9 have frequencies x and (x - 1) respectively. If their arithmetic mean is 6, what is the value of 'x'?
(a) 2
(b) 3
(c) 4
(d) 5
Answer: B

Question. What is the mean of the first 'n' natural numbers?
(a) \( n + \frac{1}{2} \)
(b) \( n(n+1) \)
(c) \( \frac{1}{2}(n+1) \)
(d) \( \frac{(n+1)}{2n} \)
Answer: C

Question. What is the arithmetic mean of 20 fours, 40 fives, 30 sixes and 10 tens?
(a) 50
(b) 25
(c) 5.6
(d) 33
Answer: C

Question. Find the value of 'x' if the mean of \( x+2, 2x+3, 3x+4 \) and \( 4x+5 \) is \( x+2 \).
(a) 2
(b) 1
(c) 3
(d) -1
Answer: D

Question. What is the value of 'n' if the mean of first 9 natural numbers is \( \frac{5n}{9} \)?
(a) 7
(b) 8
(c) 9
(d) 11
Answer: C

Question. Which of the following is true about the mode of a given data?
(a) It may or may not exist for a given data.
(b) It is always unique.
(c) It is very difficult to compute mode.
(d) We cannot calculate mode without the empirical formula.
Answer: A

Question. The A.M. of 12 observations is 15. If an observation 20 is removed, what is the arithmetic mean of the remaining observations?
(a) 14.5
(b) 13
(c) 15
(d) 13.5
Answer: A

Question. The mean weight of a group of 10 students is 25 kg and the mean weight of another group of 10 students is 35 kg. What is the mean weight of all the 20 students?
(a) 30 kg
(b) 35 kg
(c) 25 kg
(d) 20 kg
Answer: A

Question. The mean of the scores \( x_1, x_2, \dots, x_6 \) is \( \bar{x} \). What is the mean of the scores \( 5x_1, 5x_2, \dots, 5x_6 \)?
(a) \( \bar{x} + 5 \)
(b) \( \frac{\bar{x}}{5} \)
(c) \( \bar{x} - 5 \)
(d) \( 5\bar{x} \)
Answer: D

Question. Find \( \frac{x}{6} \) where 6 is the median of the scores \( \frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5} \) and \( \frac{x}{6} \).
(a) 12
(b) 4
(c) 24
(d) 6
Answer: B

Question. The mode of a data exceeds its mean by 12. By how much does its mode exceed the median?
(a) 8
(b) 12
(c) 0
(d) 10
Answer: A

Question. In a class of 19 students, 7 boys failed in a math test. The scores of those who passed are 12, 15, 17, 15, 16, 15, 19, 19, 17, 18, 18 and 19 marks. What is the median marks of the 19 students in the class?
(a) 15
(b) 12
(c) 16
(d) 19
Answer: A

Question. If the median of \( \frac{x}{5}, x, \frac{x}{4}, \frac{x}{2} \) and \( \frac{x}{3} \) (where \( x > 0 \)) is 8, what is the value of 'x'?
(a) 6
(b) 8
(c) 4
(d) 24
Answer: D

Question. The mode of the observations 5, 4, 4, 3, 5, x, 3, 4, 3, 5, 4, 3, and 5 is 3. What is their median?
(a) 3
(b) 4
(c) 5
(d) 4.5
Answer: B

Question. If the ratio of mean and median of a certain data is 2:3, what is the ratio of its mode and mean?
(a) 3 : 2
(b) 5 : 2
(c) 3 : 5
(d) 2 : 3
Answer: B

Question. What is the mode of the data 3, 6, 3, 4, 6, 4, 3, 5, 6, 5, x and \( x^2 \)?
(a) 4 or 5 only
(b) 3 or 6 only
(c) 3 or 5 only
(d) 3, 4 or 6
Answer: C

Question. What is the median of \( \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{1}{6} \) and \( \frac{7}{12} \)?
(a) \( \frac{3}{4} \)
(b) \( \frac{7}{12} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{6} \)
Answer: B

Question. What is the median of the first 100 natural numbers?
(a) 50.5
(b) 50
(c) 52
(d) 51
Answer: A

Question. If the difference of mode and median of a data is 24, what is the difference of median and mean?
(a) 24
(b) 6
(c) 12
(d) 30
Answer: C

Question. What is the arithmetic mean of 30, 20, 32, 16 and 27?
(a) 23
(b) 24
(c) 25
(d) 26
Answer: C

Question. Find the mode of 32, 20, 32, 16, 27 and 32.
(a) 20
(b) 27
(c) 30
(d) 32
Answer: D

Question. Find the median of \( 15\frac{2}{3}, 15.03, 15, 15\frac{1}{3} \) and 15.3.
(a) \( 15\frac{1}{3} \)
(b) 15.3
(c) \( 15\frac{2}{3} \)
(d) 15.03
Answer: B

Question. If for a given data median is 125.6 and mean is 128, find mode.
(a) 120.8
(b) 128.0
(c) 108.2
(d) 180.2
Answer: A

Question. What is the arithmetic mean of \( a + 2 \), a and \( a - 2 \)?
(a) \( a + 2 \)
(b) a
(c) \( a - 2 \)
(d) 3a
Answer: B

Question. The mean of 9, 11, 13, p, 18 and 19 is p. Find the value of 'p'.
(a) 12
(b) 13
(c) 14
(d) 15
Answer: C

Question. What is the mode of 10, 2, 8, 6, 7, 8, 9, 10, 10, 11 and 10?
(a) 10
(b) 12
(c) 14
(d) 8
Answer: A

Question. Which of the following is calculated using mid-values of classes?
(a) Mean
(b) Median
(c) Mode
(d) Range
Answer: A