c Which histogram shows the spread of the data more accurately?
A
aHistogram:
Distribution: Symmetric
B
b See solution.
C
c See solution.
Practice makes perfect
a Consider the given table.
Waiting Times (Minutes)
26
38
15
8
22
42
25
20
17
18
40
35
24
31
42
29
25
0
30
13
The given table represents the waiting times at a restaurant. We are asked to display the data in a histogram by using five intervals, beginning with 0-9. To do so, we first need to make a frequency table.
Waiting Times
Frequency
0-9
2
10-19
4
20-29
7
30-39
4
40-49
3
We can now display the data in a histogram. To do so, let's set the horizontal axis to be the Time and the vertical axis to be the Frequency. Finally, we will draw bars to represent the frequency of each interval. Let's do it!
We can see that the data on the right of the distribution are approximately a mirror image of the data on the left of the distribution. Therefore, the distribution is approximately symmetric.
b In the same way, let's first make a frequency table by using 10 intervals, beginning with 0-4.
Waiting Times
Frequency
0-4
1
5-9
1
10-14
1
15-19
3
20-24
3
25-29
4
30-34
2
35-39
2
40-44
3
45-49
0
Let's display the data in a histogram.
This time, we can see that the tail of the graph extends to the left and most of the data are on the right. Therefore, when the number of intervals is increased the distribution is skewed left.
c In this part we are asked which histogram best represents the data. Looking at the histograms, we can see that the histogram with more intervals shows the spread of the data more accurately. Therefore, the histogram in Part B best represents the data.
