Class 10 - Chapter 13: Statistics

Section A (1 Mark each)

Q1. Construction of a cumulative frequency table is useful in determining the:

(a) Mean (b) Median (c) Mode (d) All of the above

Q2. The median of the first 10 prime numbers is:

(a) 11 (b) 12 (c) 13 (d) 14

Q3. In the formula $\text{Median} = l + \left(\frac{\frac{n}{2} - cf}{f}\right) \times h$, $cf$ represents:

(a) cumulative frequency of the median class (b) cumulative frequency of the class succeeding the median class (c) cumulative frequency of the class preceding the median class (d) frequency of the median class

Q4. Assertion (A): The median of the data 5, 7, 9, 11, 15, 17, 19 is 11.
Reason (R): If the number of observations $n$ is odd, then the median is the $(\frac{n+1}{2})^{th}$ observation.

(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 median of the following data: 25, 34, 31, 23, 22, 26, 35, 28, 20, 32.

Solve on white paper.

Q6. If the median of the data: 6, 7, $x-2$, $x$, 17, 20, written in ascending order, is 16. Find the value of $x$.

Solve on white paper.

Q7. Find the median class of the following distribution:
Class: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 4, 4, 8, 10, 12

Solve on white paper.

Section C (3 Marks each)

Q8. Calculate the median for the following data:
Marks: 0-10, 10-20, 20-30, 30-40, 40-50
No. of Students: 5, 15, 25, 20, 7

Solve on white paper.

Q9. The median of a distribution is 24. Find the value of $p$ if the mode is 29 and mean is 21.5. Also, verify the empirical relationship.

Solve on white paper.

Section D (5 Marks)

Q10. The median of the following data is 525. Find the values of $x$ and $y$, if the total frequency is 100.
Class Interval: 0-100, 100-200, 200-300, 300-400, 400-500, 500-600, 600-700, 700-800, 800-900, 900-1000
Frequency: 2, 5, $x$, 12, 17, 20, $y$, 9, 7, 4

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Weight of Students

The weights (in kg) of 50 students of a class are given below:

Weight (kg)	40-45	45-50	50-55	55-60	60-65
No. of Students	5	17	18	8	2

(i) Form the cumulative frequency table.

(ii) Determine the median class.

(iii) Calculate the median weight of the students.

Solve on white paper.