Consider the following cumulative relative frequency distribution.
Interval Cumulative Relative Frequency
150 < x ≤ 200 0.12
200 < x ≤ 250 0.37
250 < x ≤ 300 0.51
300 < x ≤ 350 1.00
a-1. Construct the relative frequency distribution. (Round your answers to 2 decimal places.)
a-2. What proportion of the observations are more than 150 but no more than 200?
a-1. To construct the relative frequency distribution, we need to divide each cumulative relative frequency by the total number of observations.
Interval Relative Frequency
150 < x ≤ 200 0.12 - 0 = 0.12
200 < x ≤ 250 0.37 - 0.12 = 0.25
250 < x ≤ 300 0.51 - 0.37 = 0.14
300 < x ≤ 350 1.00 - 0.51 = 0.49
a-2. The cumulative relative frequency for 150 < x ≤ 200 is 0.12, which means that 12% of the observations are more than 150 but no more than 200.
a-1. To construct the relative frequency distribution, we need to find the relative frequency for each interval. Relative frequency is calculated by dividing the cumulative relative frequency by the total number of observations.
First, we can find the total number of observations by subtracting the cumulative relative frequency of the previous interval from the cumulative relative frequency of the current interval.
For the interval 150 < x ≤ 200:
Relative frequency = 0.12 - 0 = 0.12
For the interval 200 < x ≤ 250:
Relative frequency = 0.37 - 0.12 = 0.25
For the interval 250 < x ≤ 300:
Relative frequency = 0.51 - 0.37 = 0.14
For the interval 300 < x ≤ 350:
Relative frequency = 1.00 - 0.51 = 0.49
The relative frequency distribution is as follows:
Interval Relative Frequency
150 < x ≤ 200 0.12
200 < x ≤ 250 0.25
250 < x ≤ 300 0.14
300 < x ≤ 350 0.49
a-2. The proportion of the observations that are more than 150 but no more than 200 can be found by subtracting the cumulative relative frequency of the previous interval from the cumulative relative frequency of that interval:
Proportion = 0.12 - 0 = 0.12
So, 12% of the observations are more than 150 but no more than 200.