Question

34 17 32 37 38 18
35 25 28 21 27 26
31 24 23 15 21 30
(a) complete the grouped frequency distribution for
the data. (note that the class width is 6.)
shopping times
(in minutes) frequency
15 to 20
21 to 26
27 to 32
33 to 38
(b) construct a histogram for the data.
frequency
7
6
5
4
3
2
1
0
15 to 20 21 to 26 27 to 32 33 to 38
shopping times (in minutes)

Explanation:

Part (a)

Step1: Identify data in 15 - 20

Check which values are between 15 (inclusive) and 20 (inclusive). The values are 17, 18, 15. So count = 3.

Step2: Identify data in 21 - 26

Check values between 21 and 26 (inclusive). Values: 25, 21, 27 (no, 27>26), 26, 24, 23, 21. Wait, correct values: 21, 25, 26, 24, 23, 21. Wait, let's list all data: 34,17,32,37,38,18,35,25,28,21,27,26,31,24,23,15,21,30. Now for 21 - 26: 21,25,26,24,23,21. That's 6 values.

Step3: Identify data in 27 - 32

Values between 27 and 32 (inclusive): 28,27,31,30,27? Wait, data: 28,27,31,30, and 32? Wait 32 is in 27 - 32? 27 ≤ x ≤ 32. So 28,27,31,30,32. Wait no, original data: 32,28,27,31,30. Wait also 27? Wait 27 is 27, which is in 27 - 32. Wait let's count: 28,27,31,30,32. Wait no, 27 is 27, 28, 30, 31, 32. Wait also, is 27 included? Yes. So 27,28,30,31,32. Wait that's 5? Wait original data: 28,27,31,30, and 32? Wait 32 is 32, which is ≤32. So 27,28,30,31,32. Wait also, is there another? Wait the data points: 28,27,31,30,32. Wait that's 5. Wait let's check again: data points are: 34,17,32,37,38,18,35,25,28,21,27,26,31,24,23,15,21,30. So 27,28,30,31,32. That's 5 values. So frequency is 5.

Step4: Identify data in 33 - 38

Values between 33 and 38 (inclusive): 34,37,38,35. So 34,35,37,38. That's 4 values. So frequency is 4.

Part (b)

Step1: Set up axes

x - axis: shopping times (15 - 20, 21 - 26, 27 - 32, 33 - 38), y - axis: frequency (0 - 7).

Step2: Draw bars

For each class, draw a bar with height equal to its frequency. So 15 - 20: height 3, 21 - 26: height 6, 27 - 32: height 5, 33 - 38: height 4. The bars should be adjacent (no gaps, since it's a histogram for continuous data - like shopping times, treated as continuous here with class width 6).

Answer:

Shopping times (in minutes)	Frequency
21 to 26	6
27 to 32	5
33 to 38	4