Question

initial knowledge check
question 2
here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.
shopping times
(in minutes)
36 24 29 32 37
20 26 33 35 24
24 18 34 31 27
(a) complete the grouped frequency distribution for
the data. (note that the class width is 5.)
shopping times
(in minutes) frequency
17.5 - 22.5
22.5 - 27.5
27.5 - 32.5

(b) construct a histogram for the data.
frequency

Explanation:

Step1: List all data points

Data: 18, 20, 24, 24, 24, 26, 27, 29, 31, 32, 33, 34, 35, 36, 37

Step2: Count 17.5-22.5 values

Values in range: 18, 20
Frequency = $2$

Step3: Count 22.5-27.5 values

Values in range: 24, 24, 24, 26, 27
Frequency = $5$

Step4: Count 27.5-32.5 values

Values in range: 29, 31, 32
Frequency = $3$

Step5: Count 32.5-37.5 values

Values in range: 33, 34, 35, 36, 37
Frequency = $5$

Answer:

(a) Grouped Frequency Distribution:

Shopping times (in minutes)	Frequency
22.5-27.5	5
27.5-32.5	3
32.5-37.5	5

(b) Histogram Guidelines:

• On the x-axis, mark the class intervals: 17.5-22.5, 22.5-27.5, 27.5-32.5, 32.5-37.5
• On the y-axis, mark frequency values 1-6
• Draw bars for each interval with heights equal to their frequencies:
• 17.5-22.5: height = 2
• 22.5-27.5: height = 5
• 27.5-32.5: height = 3
• 32.5-37.5: height = 5