Question

the data set represents wait times (in minutes) for various services at a states department of motor vehicles locations. which wait time represents the 50th percentile? how would you interpret this?
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 18 21 1 3 3 5 5 6 10 1 22 23

which wait time represents the 50th percentile?
____ minutes
(type a whole number.)

Explanation:

Step1: Count total data points

Count all values: there are 50 data points.

Step2: Sort data in ascending order

Sorted data: $1, 1, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 10, 11, 13, 14, 14, 14, 15, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 23, 26, 26, 27$

Step3: Calculate percentile position

For 50th percentile, position $i = \frac{50}{100} \times n = 0.5 \times 50 = 25$, where $n$ is total data points.

Step4: Find value at position

The 25th value in sorted data is $8$.

Step5: Interpret the percentile

50th percentile means 50% of wait times are ≤ this value.

Answer:

Wait time for 50th percentile:

8 minutes

Interpretation:

50% of the wait times at the DMV locations are 8 minutes or less, and the other 50% are 8 minutes or more.