Question

the data set represents wait times (in minutes) for various services at a states department of motor vehicles locations. which wait times are between the 25th and 75th percentiles?

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

wait times between minutes and minutes are between the 25th and 75th percentiles.

Explanation:

Sort the dataset

Using the Percentiles and Quantiles knowledge point
First, we count and sort the \(N = 50\) data values in ascending order:
Row 1: 19, 20, 3, 7, 6, 10, 9, 10, 20, 18, 20, 10, 13, 14, 11, 14
Row 2: 17, 4, 27, 4, 8, 4, 26, 18, 21, 1, 3, 5, 5, 6, 10, 1
Row 3: 22, 23, 10, 6, 7, 1, 6, 6, 2, 4, 14, 15, 16, 4, 19, 3

Let's count the frequencies of each value:

• 1: 3 times
• 2: 1 time
• 3: 3 times
• 4: 5 times
• 5: 2 times
• 6: 5 times
• 7: 2 times
• 8: 1 time
• 9: 1 time
• 10: 5 times
• 11: 1 time
• 13: 1 time
• 14: 3 times
• 15: 1 time
• 16: 1 time
• 17: 1 time
• 18: 2 times
• 19: 2 times
• 20: 3 times
• 21: 1 time
• 22: 1 time
• 23: 1 time
• 26: 1 time
• 27: 1 time

Total count: \(3+1+3+5+2+5+2+1+1+5+1+1+3+1+1+1+2+2+3+1+1+1+1+1 = 50\).

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

Find the 25th percentile

Using the Percentiles and Quantiles knowledge point

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Find the 75th percentile

Using the Percentiles and Quantiles knowledge point

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Answer:

Wait times between <blank>5</blank> minutes and <blank>18</blank> minutes are between the 25th and 75th percentiles.