Statistics — Chapter Test | Class 9 IMO

Q1

The median of the data 24, 25, 26, x+2, x+3, 30, 31, 34 is 27.5. The value of x is:

n=8. Median = (4th + 5th)/2 = (x+2 + x+3)/2 = (2x+5)/2. So 2x+5 = 55, giving 2x = 50, x = 25.

Q2

The lower class limit of the class 25 - 35 is:

In the interval 25 - 35, the lower class limit is the starting value, which is 25.

Q3

Let m be the mid-point and l be the upper limit of a class in a continuous frequency distribution. The lower class limit of the class is:

Mid-point m = (Lower limit + Upper limit)/2. So 2m = Lower + l. Therefore, Lower limit = 2m − l.

Q4

Which of the following is not a measure of central tendency?

Mean, median, and mode measure central tendency. Range measures dispersion.

Q5

The algebraic sum of the deviations of a set of values from their mean is:

By definition, the sum of deviations of all observations from their mean is always 0. Σ(xᵢ − x̄) = 0.

Q6

In a school, 30 students obtained the following marks: 10 students got 20, 15 got 30, and 5 got 40. The mean score is:

Mean = Σ(fᵢxᵢ) / Σfᵢ = (10×20 + 15×30 + 5×40) / 30 = (200 + 450 + 200) / 30 = 850 / 30 ≈ 28.33.

Q7

In a histogram, the area of each rectangle is proportional to:

The area of a rectangle in a histogram is proportional to the corresponding class frequency.

Q8

The mean of the first 5 multiples of 3 is:

The multiples are 3, 6, 9, 12, 15. Sum = 45. Mean = 45/5 = 9.

Q9

In a histogram, the width of the rectangles is proportional to:

The width of a rectangle in a histogram corresponds to the size of the class interval on the x-axis.

Q10

Mean of 20 observations is 15.5. Later it was found that 24 was misread as 42. The corrected mean is:

Difference = 24 − 42 = −18. Correct sum = (20 × 15.5) − 18 = 310 − 18 = 292. Correct mean = 292/20 = 14.6.

Q11

If the mean of 6, 4, 7, p, and 10 is 8, then the value of p is:

Mean = (6 + 4 + 7 + p + 10)/5 = 8. So, 27 + p = 40. Therefore, p = 40 − 27 = 13.

Q12

A shopkeeper sells 5 shirts of size 38, 12 of size 40, 8 of size 42, and 2 of size 44. The modal shirt size sold is:

Size 40 has the highest frequency (12). Thus, the mode is 40.

Q13

In a cricket match, Virat scored 45, 60, 30, 85, and 80 runs in 5 innings. What is the median of his scores?

Arranged in order: 30, 45, 60, 80, 85. The middle value (3rd term) is 60.

Q14

A taxi driver in Delhi earns ₹500, ₹450, ₹600, ₹400, and ₹550 in 5 days. What is the median earning?

Arranging in ascending order: 400, 450, 500, 550, 600. The median (middle value) is ₹500.

Q15

The weights of 5 students in kg are 42, 45, 48, 51, 54. The range of their weights is:

Range = Maximum value − Minimum value = 54 − 42 = 12.