here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.\nshopping…
here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store.\nshopping times (in minutes)\n32 18 29 27 37\n35 35 23 28 35\n33 19 22 20 24\n(a) complete the grouped frequency distribution for the data. (note that the class width is 5.)\nshopping times (in minutes) frequency\n18 to 22 \n23 to 27 \n28 to 32 \n33 to 37 \n(b) construct a histogram for the data.\nfrequency\n6\n5\n4\n3\n2\n1\n0\n18 to 22 23 to 27 28 to 32 33 to 37\nshopping times (in minutes)
Answer
Explanation:
Step1: Count data in 18 - 22
Count numbers in the range 18 - 22 from the data set {32, 18, 29, 27, 37, 35, 35, 23, 28, 35, 33, 19, 22, 20, 24}. The numbers are 18, 19, 22, 20, so the frequency is 4.
Step2: Count data in 23 - 27
Count numbers in the range 23 - 27. The numbers are 23, 27, 24, so the frequency is 3.
Step3: Count data in 28 - 32
Count numbers in the range 28 - 32. The numbers are 29, 28, 32, so the frequency is 3.
Step4: Count data in 33 - 37
Count numbers in the range 33 - 37. The numbers are 37, 35, 35, 35, 33, so the frequency is 5.
Answer:
| Shopping times (in minutes) | Frequency |
|---|---|
| 18 to 22 | 4 |
| 23 to 27 | 3 |
| 28 to 32 | 3 |
| 33 to 37 | 5 |
For part (b), to construct the histogram:
- On the x - axis, label the intervals 18 to 22, 23 to 27, 28 to 32, 33 to 37.
- On the y - axis, label the frequency from 0 to 6.
- Draw a bar for each interval with height corresponding to the frequency:
- For the interval 18 to 22, the bar height is 4.
- For the interval 23 to 27, the bar height is 3.
- For the interval 28 to 32, the bar height is 3.
- For the interval 33 to 37, the bar height is 5.