Question

the data set represents wait times (in minutes) for various services at a states department of motor vehicles locations. find the percentile that corresponds to a wait time of 4 minutes
5 6 10 1 22 23 10 6 7 2 1 6 6 2 4 14
15 16 4 19 3 19 26 5 3 4 7 6 10 9 10 20
18 3 20 10 13 14 11 14 17 4 27 4 8 4 3 26
a wait time of 4 minutes corresponds to about a percentile of
(round to the nearest whole number as needed.)

Explanation:

Step1: Count total data points

Count all values: there are 50 data points, so $n=50$.

Step2: Count values ≤ 4

Count numbers less than or equal to 4: 1,1,2,2,3,3,3,3,4,4,4,4,4. That's 13 values, so $k=13$.

Step3: Apply percentile formula

Use percentile formula: $\text{Percentile} = \frac{k}{n} \times 100$
$\text{Percentile} = \frac{13}{50} \times 100$

Step4: Calculate and round

$\frac{13}{50} \times 100 = 26$, which is a whole number.

Answer:

26