Consider the following relative frequency distribution:
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.
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
To construct the frequency distribution from the given relative frequency distribution, we need to multiply the relative frequencies by the sample size and round them to the nearest whole number.
Given:
Sample size (n) = 49
To find the frequency for each interval, we multiply the relative frequency by the sample size (49) and round to the nearest whole number.
Interval Relative Frequency Frequency
−20 < x ≤ −10 0.26 0.26 * 49 ≈ 12.74 ≈ 13
−10 < x ≤ 0 0.22 0.22 * 49 ≈ 10.78 ≈ 11
0 < x ≤ 10 0.26 0.26 * 49 ≈ 12.74 ≈ 13
10 < x ≤ 20 0.07 0.07 * 49 ≈ 3.43 ≈ 3
20 < x ≤ 30 0.19 0.19 * 49 ≈ 9.31 ≈ 9
So, the frequency distribution is as follows:
Interval Frequency
−20 < x ≤ −10 13
−10 < x ≤ 0 11
0 < x ≤ 10 13
10 < x ≤ 20 3
20 < x ≤ 30 9