Class 10 - Chapter 13: Statistics

Section A (1 Mark each)

Q1. The algebraic sum of the deviations of a frequency distribution from its mean is always:

(a) greater than 0 (b) less than 0 (c) 0 (d) a non-zero constant

Q2. While computing mean of grouped data, we assume that the frequencies are:

(a) evenly distributed over all the classes (b) centred at the classmarks of the classes (c) centred at the upper limits of the classes (d) centred at the lower limits of the classes

Q3. If the mean of the following distribution is 2.6, then the value of $y$ is:
Variable (x): 1, 2, 3, 4, 5
Frequency (f): 4, 5, y, 1, 2

(a) 3 (b) 8 (c) 13 (d) 24

Q4. Assertion (A): The mean of the first $n$ odd natural numbers is $n$.
Reason (R): Mean = $\frac{\text{Sum of observations}}{\text{Number of observations}}$.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. Find the mean of the first 5 prime numbers.

Solve on white paper.

Q6. The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

Solve on white paper.

Q7. If $x_i$'s are the mid-points of the class intervals of grouped data, $f_i$'s are the corresponding frequencies and $\bar{x}$ is the mean, then find the value of $\sum (f_i x_i - \bar{x})$.

Solve on white paper.

Section C (3 Marks each)

Q8. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy Rate (%): 45-55, 55-65, 65-75, 75-85, 85-95
Number of Cities: 3, 10, 11, 8, 3

Solve on white paper.

Q9. The mean of the following distribution is 18. Find the missing frequency $f$.
Class Interval: 11-13, 13-15, 15-17, 17-19, 19-21, 21-23, 23-25
Frequency: 7, 6, 9, 13, $f$, 5, 4

Solve on white paper.

Section D (5 Marks)

Q10. Calculate the mean of the following frequency distribution using the Step-Deviation method:
Class Interval: 0-50, 50-100, 100-150, 150-200, 200-250, 250-300
Frequency: 17, 35, 43, 40, 21, 24

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Mileage of Cars

A survey was conducted to find the mileage (in km/l) of 50 cars of the same model. The data obtained is given below:

Mileage (km/l)	10-12	12-14	14-16	16-18	18-20
No. of Cars	7	12	18	8	5

(i) Find the class mark of the class interval 14-16.

(ii) Find the mean mileage of the cars.

(iii) If the manufacturer improves the engine efficiency such that the mileage of every car increases by 2 km/l, what will be the new mean mileage?

Solve on white paper.