Consider the following cumulative relative frequency distribution.
Interval Cumulative Relative Frequency
150 < x ≤ 200 0.12
200 < x ≤ 250 0.31
250 < x ≤ 300 0.57
300 < x ≤ 350 1.00
a-1. Construct the relative frequency distribution. (Round your answers to 2 decimal places.)
To construct the relative frequency distribution, we can subtract each interval's cumulative relative frequency from the previous interval's cumulative relative frequency.
Interval | Cumulative Relative Frequency | Relative Frequency
150 < x ≤ 200 | 0.12 | 0.12
200 < x ≤ 250 | 0.31 - 0.12 = 0.19 | 0.19
250 < x ≤ 300 | 0.57 - 0.31 = 0.26 | 0.26
300 < x ≤ 350 | 1.00 - 0.57 = 0.43 | 0.43
To construct the relative frequency distribution, we need to calculate the relative frequency for each interval.
The relative frequency is the proportion of the total frequency (or cumulative relative frequency) accounted for by each interval. It can be calculated by subtracting the cumulative relative frequency of the previous interval from the cumulative relative frequency of the current interval.
For example, for the interval 150 < x ≤ 200, the relative frequency is:
Relative frequency = Cumulative relative frequency (200 < x ≤ 250) - Cumulative relative frequency (150 < x ≤ 200)
= 0.31 - 0.12
= 0.19
Similarly, we can calculate the relative frequencies for the other intervals:
For the interval 200 < x ≤ 250:
Relative frequency = Cumulative relative frequency (250 < x ≤ 300) - Cumulative relative frequency (200 < x ≤ 250)
= 0.57 - 0.31
= 0.26
For the interval 250 < x ≤ 300:
Relative frequency = Cumulative relative frequency (300 < x ≤ 350) - Cumulative relative frequency (250 < x ≤ 300)
= 1.00 - 0.57
= 0.43
For the interval 300 < x ≤ 350:
Relative frequency = Cumulative relative frequency (300 < x ≤ 350) - Cumulative relative frequency (300 < x ≤ 350) [Since it's the last interval]
= 1.00 - 1.00
= 0.00
So, the relative frequency distribution is:
Interval Relative Frequency
150 < x ≤ 200 0.19
200 < x ≤ 250 0.26
250 < x ≤ 300 0.43
300 < x ≤ 350 0.00