1. determine the cumulative frequency, relative frequency, and relative cumulative frequency for the…
1. determine the cumulative frequency, relative frequency, and relative cumulative frequency for the following data and then answer the questions. round four decimal places.\n\n| price interval | frequency | cumulative frequency | relative frequency $rf=\frac{f}{n}$ | relative cumulative frequency |\n| ---- | ---- | ---- | ---- | ---- |\n| $100 - $149.99 | 11 | 11 | 0.2115 | 0.2115 |\n| $150 - $199.99 | 15 | 26 | 0.2884 | 0.7115 |\n| $200 - $249.99 | 6 | 32 | 0.1154 | 0.8269 |\n| $250 - $299.99 | 5 | 37 | 0.0961 | 0.9231 |\n| $300 - $349.99 | 11 | 48 | 0.2115 | 0.9231 |\n| $350 - $399.99 | 4 | 52 | 0.0769 | 1.0000 |\n\n$n = 52$\n\na. how many prices are at or below $300 - $349.99?\nb. how many prices are at or above $200 - $249.99?\nc. how many prices are between $150 - $199.99 to $300 - $349.99?\nd. which price ranges have a relative frequency greater than.05 and less than.12?\ne. interpret the relative frequency of $200 - $249.99 in terms of a percent.\nf. interpret the relative cumulative frequency up to $250 - $299.99 in terms of a percent.
Answer
Explanation:
Step1: Recall cumulative frequency concept
The cumulative frequency up to a certain interval gives the number of data - points at or below that interval.
Step2: Answer part a
The cumulative frequency for the interval $300 - 349.99$ is $48$. So, the number of prices at or below $300 - 349.99$ is $48$.
Step3: Answer part b
The total number of data - points $N = 52$. The cumulative frequency up to the interval $199.99$ is $26$. So the number of prices at or above $200 - 249.99$ is $52−26 = 26$.
Step4: Answer part c
The cumulative frequency up to $199.99$ is $26$ and up to $349.99$ is $48$. So the number of prices between $150 - 199.99$ and $300 - 349.99$ is $48 - 11=37$.
Step5: Answer part d
The relative frequencies are:
- For $100 - 149.99$: $0.2115$
- For $150 - 199.99$: $0.2884$
- For $200 - 249.99$: $0.1154$
- For $250 - 299.99$: $0.0961$
- For $300 - 349.99$: $0.2115$
- For $350 - 399.99$: $0.0769$ The price ranges with relative frequency greater than $0.05$ and less than $0.12$ are $200 - 249.99$ and $250 - 299.99$ and $350 - 399.99$.
Step6: Answer part e
The relative frequency of $200 - 249.99$ is $0.1154$. In terms of a percent, it is $0.1154\times100 = 11.54%$.
Step7: Answer part f
The relative cumulative frequency up to $250 - 299.99$ is $\frac{37}{52}\approx0.7115$. In terms of a percent, it is $0.7115\times 100 = 71.15%$.
Answer:
a. $48$ b. $26$ c. $37$ d. $200 - 249.99$, $250 - 299.99$, $350 - 399.99$ e. $11.54%$ f. $71.15%$