Question

here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.
shopping times
(in minutes)
33 22 37 35 20
19 35 23 28 29
24 35 32 18 27
(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
6
5
4
3
2
1
0
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: 20, 19, 18. That's 3 values.

Step2: Count 23 - 27

Data points: 22, 23, 24, 27. Wait, 22? No, 23,24,27 and 22 is in 18 - 22? Wait, 23,24,27 and 23,24,27, also 22 is 22, which is 18 - 22? Wait, 18 - 22 includes 18,19,20,21,22. So 22 is in 18 - 22? Wait, no: 18 to 22: 18,19,20,21,22. So data points: 20,19,18,22. Wait, original data: 33,22,37,35,20,19,35,23,28,29,24,35,32,18,27. So 18,19,20,22: that's 4? Wait, 18,19,20,22: 4 values? Wait, 18 (1), 19 (2), 20 (3), 22 (4). Oh, I missed 22. So 18 - 22: 18,19,20,22 → 4? Wait no, 22 is 22, which is ≤22. So 18,19,20,22: 4? Wait original data: 33,22,37,35,20,19,35,23,28,29,24,35,32,18,27. Let's list all:

18,19,20,22,23,24,27,28,29,32,33,35,35,35,37.

Now group:

18 - 22: 18,19,20,22 → 4? Wait 18,19,20,22: 4 values.

23 - 27: 23,24,27 → 3? Wait 23,24,27: 3? Wait 23,24,27, and 23,24,27: 3 values? Wait 23,24,27: 3.

28 - 32: 28,29,32 → 3? 28,29,32: 3.

33 - 37: 33,35,35,35,37 → 5? 33,35,35,35,37: 5.

Wait let's count again:

18 - 22: 18,19,20,22 → 4.

23 - 27: 23,24,27 → 3 (since 23-27: 23,24,25,26,27; so 23,24,27: 3).

28 - 32: 28,29,32 → 3 (28-32:28,29,30,31,32; so 28,29,32: 3).

33 - 37: 33,35,35,35,37 → 5 (33-37:33,34,35,36,37; so 33,35,35,35,37: 5).

Wait 4 + 3 + 3 + 5 = 15, which matches the number of data points (15). So:

18 - 22: 4

23 - 27: 3

28 - 32: 3

33 - 37: 5

Answer:

For part (a), the frequencies are: 18 to 22: 4, 23 to 27: 3, 28 to 32: 3, 33 to 37: 5.

For part (b), the histogram will have bars with heights 4, 3, 3, 5 for the respective intervals.