Statistics — Chapter Test | Class 10 IMO

Q1

The median of 3, 5, 7, 9 and 11 is:

The middle value of the ordered data is 7.

Q2

In the step-deviation method, u is defined as:

u = (x − a)/h, where h is the class size.

Q3

For grouped data, the median lies in the class where the cumulative frequency first reaches or exceeds:

The median class is where the cumulative frequency first reaches n/2.

Q4

The median can be read from a graph as the x-value where the less-than and more-than ogives:

The two ogives cross at the median.

Q5

For a perfectly symmetric distribution, mean, median and mode are:

Symmetry makes the three measures coincide.

Q6

Two groups have 10 and 15 members with means 20 and 30. The combined mean is:

(10 × 20 + 15 × 30) ÷ 25 = (200 + 450) ÷ 25 = 650 ÷ 25 = 26.

Q7

For a symmetric data set with classes 0–10, 10–20, 20–30, 30–40, 40–50 having frequencies 4, 6, 10, 6, 4, the mean is:

Σfx = 750 and Σf = 30, so mean = 750 ÷ 30 = 25.

Q8

If each observation of a data set is increased by 5, the mean:

Adding a constant to every value shifts the mean by that constant.

Q9

An ogive is the graph of:

An ogive plots cumulative frequencies.

Q10

For classes 10–20, 20–30, 30–40 with frequencies 6, 10, 6, the mode is:

Modal class 20–30 with f1 = 10, f0 = 6, f2 = 6: mode = 20 + ((10 − 6)/(20 − 6 − 6)) × 10 = 25.

Q11

The empirical relationship between mean, median and mode is:

Mode = 3 Median − 2 Mean, i.e. 3 Median = Mode + 2 Mean.

Q12

A shop sells shoes of sizes 6, 7, 7, 8, 7, 9 and 7. The modal size is:

Size 7 sells most often, so it is the mode.

Q13

A batsman scores 30, 45, 0, 60 and 15 in five innings. His mean score is:

(30 + 45 + 0 + 60 + 15) ÷ 5 = 150 ÷ 5 = 30.

Q14

A shopkeeper records the number of bags sold each day for a week as 5, 8, 8, 10, 8, 6 and 8. The mode is:

8 occurs most often.

Q15

The mode of 7, 8, 8, 9, 9, 9, 10 is:

9 occurs three times, more than any other value.