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 3 minutes.
8 4 3 26 18 21 1 3 3 5 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
a wait time of 3 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 45 data points, so $n=45$.

Step2: Count values ≤ 3

List values ≤3: 1,1,1,2,2,3,3,3,3,3,3. Total: $k=11$.

Step3: Calculate percentile

Use percentile formula: $\text{Percentile} = \frac{k}{n} \times 100$
$\text{Percentile} = \frac{11}{45} \times 100 \approx 24.44$

Step4: Round to whole number

Round 24.44 to nearest integer: 24.

Answer:

24