Question

an auto repair shop records how far each vehicle they receive has been driven. the data for their most recent 23 vehicles is shown in the histogram below. what interval contains the 83rd percentile for this data? choose 1 answer:

Explanation:

Step1: Calculate the index

The formula for the index of the $p$ - th percentile is $i=\frac{p}{100}\times n$, where $p = 83$ and $n=23$. So $i=\frac{83}{100}\times23=19.09$.

Step2: Cumulative - frequency calculation

We calculate the cumulative - frequency. The frequencies from left to right are $3,4,5,6,3,2$. The cumulative - frequencies are: for the first interval ($0 - 50$) is $3$; for the second interval ($50 - 100$) is $3 + 4=7$; for the third interval ($100 - 150$) is $7+5 = 12$; for the fourth interval ($150 - 200$) is $12 + 6=18$; for the fifth interval ($200 - 250$) is $18+3 = 21$; for the sixth interval ($250 - 300$) is $21 + 2=23$.

Step3: Determine the percentile interval

Since the index $i = 19.09$ and the cumulative - frequency first exceeds $19.09$ when we reach the fifth interval ($200 - 250$).

Answer:

$200 - 250$ (thousands of kilometers)