Question

here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.
shopping times
(in minutes)
37 27 19 23 35
29 28 33 32 22
20 24 35 35 18
(a) complete the grouped frequency distribution for the data. (note that the class width is 5.)
shopping times (in minutes) frequency
18 to 22
23 to 27
28 to 32
33 to 37
(b) construct a histogram for the data.
frequency
18 to 22 23 to 27 28 to 32 33 to 37
shopping times (in minutes)

Explanation:

Step1: Count 18 - 22

Check each data point: 18,19,20,22. So count is 4 (18,19,20,22).

Step2: Count 23 - 27

Data points:23,24,27. Wait, 23,24,27? Wait original data: 23,24,27? Wait the data is 37,27,19,23,35,29,28,33,32,22,20,24,35,35,18. Let's list all:

18,19,20,22 (18 - 22: 18,19,20,22 → 4)

23,24,27 (23 - 27: 23,24,27? Wait 27 is included? Wait class is 23 to 27, so 23,24,27? Wait 27 is ≤27. Wait data points:23,24,27? Wait also 27 is in the data. Wait let's list all data:

18,19,20,22,23,24,27,28,29,32,33,35,35,35,37. Wait 15 data points.

Now 23 - 27: 23,24,27 → that's 3? Wait 23,24,27: 3 numbers? Wait 27 is included. Then 28 - 32: 28,29,32 → 3? Wait 28,29,32: 3? Wait no, 28,29,32 and also 28,29,32: wait 28,29,32: that's 3? Wait no, 28,29,32: 3 numbers? Wait 28,29,32: 3? Wait 28,29,32: 3. Then 33 - 37: 33,35,35,35,37 → 5? Wait 33,35,35,35,37: 5 numbers. Wait let's recount:

18 - 22: 18,19,20,22 → 4 (correct, 4 numbers)

23 - 27: 23,24,27 → 3? Wait 23,24,27: 3. Wait but 27 is in the data. Then 28 - 32: 28,29,32 → 3? Wait 28,29,32: 3. Then 33 - 37: 33,35,35,35,37 → 5. Let's check total: 4 + 3 + 3 + 5 = 15. Correct.

Wait wait, maybe I made a mistake. Let's list all data points:

1. 18

1. 19

1. 20

1. 22

1. 23

1. 24

1. 27

1. 28

1. 29

1. 32

1. 33

1. 35

1. 35

1. 35

1. 37

Now:

18 - 22: 18,19,20,22 → 4 (indices 1 - 4)

23 - 27: 23,24,27 → indices 5,6,7 → 3

28 - 32: 28,29,32 → indices 8,9,10 → 3

33 - 37: 33,35,35,35,37 → indices 11,12,13,14,15 → 5

Yes, 4 + 3 + 3 + 5 = 15. So:

18 to 22: 4

23 to 27: 3

28 to 32: 3

33 to 37: 5

Step3: Verify

Check each class:

18 - 22: 18,19,20,22 → 4 ✔️

23 - 27: 23,24,27 → 3 ✔️

28 - 32: 28,29,32 → 3 ✔️

33 - 37: 33,35,35,35,37 → 5 ✔️

Answer:

For the grouped frequency distribution:

• 18 to 22: 4

• 23 to 27: 3

• 28 to 32: 3

• 33 to 37: 5

(For the histogram, the bars would have heights 4, 3, 3, 5 respectively for the classes 18 - 22, 23 - 27, 28 - 32, 33 - 37)