Answer:
See attachment for histogram
The histogram is left skewed
Step-by-step explanation:
Given
[tex]40, 47, 37, 42, 46, 31, 50, 41, 17[/tex]
[tex]43, 46, 45, 21, 43, 45, 23, 49, 50[/tex]
[tex]48, 26, 42, 46, 35, 52, 27, 51, 31[/tex]
[tex]44, 35, 27, 46, 39, 33, 50, 45, 50[/tex]
Solving (a): Construct a histogram
First, we construct a frequency table
Calculate Range
[tex]Range = Highest - Least[/tex]
[tex]Range = 52 - 17[/tex]
[tex]Range = 35[/tex]
Using a class width of 5, we have the following classes:
[tex]17 - 22; 23 - 28; 29 - 34; 35 - 40; 41 - 46; 47 - 52[/tex]
So, the frequency table is:
[tex]\begin{array}{ccccccc}{Class} & {17-22} & {23-28} & {29-34} & {35-40} & {41-46} & {47-52} \ \\ {Count} & {2} & {4} & {3} & {5} & {13} & {9} \ \end{array}[/tex]
See attachment for histogram
From the attached histogram, we can see that the height of the bars of the histogram tend to increase towards the left.
Hence, the shape of the histogram is left skewed
