Class 10 - Chapter 13: Statistics

Section A (1 Mark each)

Q1. The empirical relationship between the three measures of central tendency is:

(a) 3 Median = Mode + 2 Mean (b) 2 Median = Mode + 3 Mean (c) 3 Median = Mode - 2 Mean (d) Median = Mode + Mean

Q2. The mode of the data 5, 7, 9, 11, 13, 15, 17, 9, 19, 9 is:

(a) 9 (b) 11 (c) 13 (d) 17

Q3. In the formula for finding mode of grouped data, $l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h$, the symbol $f_0$ represents:

(a) frequency of modal class (b) frequency of class preceding modal class (c) frequency of class succeeding modal class (d) class mark of modal class

Q4. Assertion (A): The mode of a frequency distribution can be determined graphically from a Histogram.
Reason (R): The highest bar in a histogram represents the class with maximum frequency.

(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. If the mean of a distribution is 15 and its median is 18, then find its mode.

Solve on white paper.

Q6. Find the mode of the following data:
Class: 0-20, 20-40, 40-60, 60-80
Frequency: 15, 6, 18, 10

Solve on white paper.

Q7. What is the modal class of the following distribution?
Marks: Below 10, Below 20, Below 30, Below 40, Below 50
No. of students: 3, 12, 27, 57, 75

Solve on white paper.

Section C (3 Marks each)

Q8. Find the mode of the following frequency distribution:
Class: 10-20, 20-30, 30-40, 40-50, 50-60
Frequency: 12, 35, 45, 25, 13

Solve on white paper.

Q9. The mode of the following distribution is 55. Find the value of $x$.
Class: 0-15, 15-30, 30-45, 45-60, 60-75, 75-90
Frequency: 6, 7, $x$, 15, 10, 8

Solve on white paper.

Section D (5 Marks)

Q10. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
Lifetimes (in hours): 0-20, 20-40, 40-60, 60-80, 80-100, 100-120
Frequency: 10, 35, 52, 61, 38, 29
Determine the modal lifetimes of the components.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Height of Students

A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data was obtained:

Height (in cm)	135-140	140-145	145-150	150-155	155-160	160-165
No. of Girls	4	7	18	11	6	5

(i) Identify the modal class and the median class.

(ii) Calculate the Mode of the data.

(iii) If the mean height is 149.02 cm, compare it with the mode.

Solve on white paper.