CBSE Class 10 Statistics Sure Shot Questions Set 06

Question. What is the mean of n numbers \(x_1, x_2, \dots, x_n\)?
Answer: \( \frac{\sum x_i}{n} \)

Question. What is the mean of observations \(x_1, x_2, \dots, x_n\) with frequencies \(f_1, f_2, \dots, f_n\)?
Answer: \( \frac{\sum x_i f_i}{\sum f_i} \)

Question. What is the mean of the data 6, 8, 7, 3, 2?
Answer: 5.2

Question. The number of children of 10 families of a locality are 2, 4, 3, 4, 2, 0, 3, 5, 1, 1. What is the mean number of children per family?
Answer: 2.5

Question. What is the mean of data x, x + 2, x + 4, x + 6, x + 8 ?
Answer: x + 4

Question. Find the mean of first five natural numbers.
Answer: 3

Question. For the numbers 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9 find \( \sum_{i=1}^{10} (x_i - \bar{x}) \).
Answer: 0

Question. Find the frequencies:-
Below 10: 5
Below 20: 9
Below 30: 17
Below 40: 29
Below 50: 45
Answer: 5, 4, 8, 12, 16

Question. Find the missing frequency p if \( \sum f_i = 30 \) and
Class Marks : 12 14 16 18 20
Frequencies : 3 6 9 p 4
Answer: 8

Question. The mean of 20 numbers is 17. If 3 is added to every number, then find the new mean.
Answer: 20

Question. If \( \bar{x} \) is the mean of n observations \(x_1, x_2, \dots, x_n\) then find \( \sum_{i=1}^{n} (x_i - \bar{x}) \).
Answer: 0

Question. Find the mean of first five prime numbers.
Answer: 5.6

Question. The mean of 6, 4, 7, x and 14 is 8. Find x.
Answer: 9

Question. Find the frequencies of the data:-
Above 0: 80
Above 10: 77
Above 20: 72
Above 30: 65
Above 40: 55
Answer: 3, 5, 7, 10

Question. The mean of 5 numbers is 18. If one number is excluded their mean is 16. Find the excluded number.
Answer: 26

Question. In the following data what is \( \sum f_i \)?
x: 10 15 20 25
f: 5 10 p 8
Answer: 23 + p

Question. Find the mean of first five odd natural numbers.
Answer: 5

Question. The scores of two batsmen A and B in five innings of a test series are
A : 55 60 60 65 45
B : 120 80 30 20 10
What is the mean score of batsman B?
Answer: 52

Question. Find the sum of deviations of the variate values 3, 4, 6, 8, 14 from their mean.
Answer: 0

Question. The mean of 20 numbers is 35. If each number is divided by 5 then what is the new mean.
Answer: 7

Question. What is the mean of first five composite numbers?
Answer: 7.4

Question. In the following data what is \( f_i x_i \)?
x : 5 10 15 20
f : 7 p 8 4
xf : 35 10p 120 80
Answer: 235 + 10p

Question. The mean of 40 observations was 160. It was detected on rechecking that the value of 165 was wrongly copied as 125 for computing of mean. Find the correct mean.
Answer: 161

Question. If \( u_i = \frac{x_i - 25}{10} \), \( \sum f_i u_i = 20 \) and \( \sum f_i = 100 \) then find the value of \( \bar{x} \).
Answer: 27

Question. In a factory the daily wages of 5 workers are 20, 40, 42, 45 and 33. If the daily wages of each worker is increased by Rs. 5, find the mean wage.
Answer: 41

Question. What is the median of numbers:- 16, 17, 18, 20, 21, 24, 25, 26, 28?
Answer: 21

Question. Find the median of the numbers :– 7, 8, 9, 11, 13, 14, 15, 16
Answer: 12

Question. What is the value of x if the median of given data is 27.5?
24, 25, 26, x + 2, x + 3, 30, 31, 34
Answer: x = 25

Question. What is the mode of the given data?
2, 2, 3, 5, 5, 7, 7, 2, 3, 4, 7, 2
Answer: 2

Question. Find the value of x if the mode of the data is 18.
16, 18, 17, 16, 18, x, 19, 17, 14
Answer: 18

Question. If mode of the data (given) is 43 then what is the value of x + 2?
34, 43, 48, 43, x, 48, 60, 64
Answer: 45

Question. If 27 is taken out from the given data then what is the new median?
20, 24, 25, 26, 27, 28, 29, 30
Answer: 26

Question. When 93 is added to the data given below what is the new median?
43, 47, 51, 53, 67, 79, 84, 97
Answer: 67

Question. If the probability of winning a game is 0.7, what is the probability of losing it?
Answer: 0.3

Question. A pair of dice is thrown once. Find the probability of getting a sum of 11.
Answer: \( \frac{1}{18} \)

Question. A bag contains 7 red, 5 white and 9 black balls. One ball is drawn from the bag. Find the probability that it is not a red ball.
Answer: \( \frac{2}{3} \)

Question. A bag contains 20 cards numbering 1,2,3, . . . . . . . . . . , 20. One card is drawn from the bag. Find the probability that it has a prime number.
Answer: \( \frac{2}{5} \)

Question. How many face cards are there in a well shuffled pack of cards?
Answer: 12

Question. In 1000 lottery tickets there are 5 prize winning tickets. Find the probability of winning a prize if a person buys one ticket.
Answer: \( \frac{1}{200} \)

Question. It is known that in a box of 600 screws, 42 screws are defective. One screw is taken out at random from this box. Find the probability that it is a good screw.
Answer: \( \frac{93}{100} \)

Question. Five male and three female candidates are available for selection of one manager in a company. Find the probability that female is selected.
Answer: \( \frac{3}{8} \)

Question. What are all the possible outcomes when a coin is tossed twice?
Answer: HH, HT, TH, TT

Question. A child has a block in the shape of a cube with one letter written on each face as shown below:- A B C B D D. The cube is thrown once. Find the probability of getting B or C.
Answer: \( \frac{1}{2} \)

Question. If E be an event such that P(E) = \( \frac{3}{7} \), what is P (not E) equal to?
Answer: \( \frac{4}{7} \)

Question. A bag contains 5 red balls and n green balls. If the probability of drawing a green ball is three times that of a red ball then what is the value of n?
Answer: 15

Question. If from the well shuffled pack of cards all the aces are removed, find the probability of getting red card.
Answer: \( \frac{1}{2} \)

Question. From the data (1, 4, 9, 16, 25, 29) if 29 is removed. What is the probability of getting a prime number?
Answer: Zero

Question. What is the probability of getting a total of less than 12 in the throws of two dice?
Answer: \( \frac{35}{36} \)

Question. Cards marked with numbers 1, 2, 3, . . . . . . , 100 are placed in a bag and mixed thoroughly. One card is drawn. What is the probability that card drawn has an even number?
Answer: \( \frac{1}{2} \)

Question. A card is drawn from an ordinary pack of playing cards and a person bets that it is a spade or an ace. What are the odds against his winning the bet?
Answer: \( \frac{9}{13} \)