Question

the data set represents wait times (in minutes) for various services at a states department locations. which wait time represents the 50th percentile? how would you interpret this?3 3 5 5 6 10 1 22 23 10 6 7 2 1 62 4 14 15 16 4 19 3 19 26 5 3 4 7 69 10 20 18 3 20 10 13 14 11 14 17 4 27 4which wait time represents the 50th percentile?8 minutes(type a whole number.)how would you interpret this?a. this is the mode of the wait times.b. at least 50% of wait times are greater than this wait time.c. about 50% of wait times are less than this wait time.d. this is the mean of the wait times.

Explanation:

Step1: Count total data points

Count all wait times: there are 45 data points.

Step2: Calculate percentile position

Use formula for percentile rank: $i = \frac{P}{100} \times n$, where $P=50$, $n=45$.
$i = \frac{50}{100} \times 45 = 22.5$

Step3: Sort data & find value

Sort data in ascending order:
1,1,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,6,6,6,7,7,9,10,10,10,11,13,14,14,14,15,16,17,18,19,19,20,20,22,23,26,27
Round up $i=22.5$ to 23rd position. The 23rd value is 9.

Step4: Interpret 50th percentile

The 50th percentile (median) means ~50% of data is below it.

Answer:

9 minutes
C. About 50% of wait times are less than this wait time.