Consider the following relative frequency distribution:

Question

Interval Relative Frequency
−20 < x ≤ −10 0.26
−10 < x ≤ 0 0.22
0 < x ≤ 10 0.26
10 < x ≤ 20 0.07
20 < x ≤ 30 0.19


a-1. Suppose this relative frequency distribution is based on a sample of 49 observations. Construct the frequency distribution.

Answer 1

To construct the frequency distribution, we need to multiply the relative frequencies by the sample size.

First, let's calculate the frequency (f) for each interval. The frequency is given by:

f = relative frequency * sample size

For the interval -20 < x ≤ -10, the frequency can be calculated as:
f = 0.26 * 49 = 12.74 ≈ 13

For the interval -10 < x ≤ 0, the frequency can be calculated as:
f = 0.22 * 49 = 10.78 ≈ 11

For the interval 0 < x ≤ 10, the frequency can be calculated as:
f = 0.26 * 49 = 12.74 ≈ 13

For the interval 10 < x ≤ 20, the frequency can be calculated as:
f = 0.07 * 49 = 3.43 ≈ 3

For the interval 20 < x ≤ 30, the frequency can be calculated as:
f = 0.19 * 49 = 9.31 ≈ 9

Now, we can construct the frequency distribution table as follows:

Interval Frequency
−20 < x ≤ −10 13
−10 < x ≤ 0 11
0 < x ≤ 10 13
10 < x ≤ 20 3
20 < x ≤ 30 9