The following data represent salaries, in thousands of dollars, for employees of a small company. Notice the data have been sorted in increasing order.
54 55 55 57 57 59 60 65 65 65 66 68 68 69 69 70 70 70 75 75 75 75 77 82 82 82 88 89 89 91 91 97 98 98 98 280
Make a histogram using the class boundaries 53.5, 99.5, 145.5, 191.5, 237.5, 283.5.

Step-by-step explanation:

Hello!

To make the histogram you have order the data in a distribution table.

The class marks the middle of each class interval defined for the variable, it is obtained by adding the boundaries and then dividing it by two.

When arranging data in a table of frequencies where the possible values of the variable are classified in class intervals, you have to take into account that each class interval has to have the same amplitude (width). A characteristic of the class marks is that the distance between them is equal to the amplitude of the class intervals.

To arrange the given data into each class you have to define the intervals first. So first step will be calculate the amplitude of the intervals using the given class marks:

a= 99.5-53.5= 46

Then the semiamplitude of each interval will be:

d= a/2= 46/2= 23

You will obtain each interval by adding and subtracting the semiamplitude (d) from the class mark (x')

x' ± d

Class intervals:

53.5 ± 23= [30.5;76.5)

99.5 ± 23= [76.5;122.5)

145.5 ± 23= [122.5;168.5)

191.5 ± 23= [168.5;214.5)

237.5 ± 23= [214.5;260.5)

283.5 ± 23= [260.5;306.5)

Now that the intervals are defined, you can "count" how many observed values are included in each interval (absolute frequency of each interval "f(x)")

Afterwards you will be able to make the histogram.

54 55 55 57 57 59 60 65 65 65 66 68 68 69 69 70 70 70 75 75 75 75 77 82 82 82 88 89 89 91 91 97 98 98 98 280

[30.5;76.5): 54 55 55 57 57 59 60 65 65 65 66 68 68 69 69 70 70 70 75 75 75 75 ⇒ f(x)= 22

[76.5;122.5): 77 82 82 82 88 89 89 91 91 97 98 98 98 ⇒ f(x)= 13

[122.5;168.5): ⇒ f(x)= 0

[168.5;214.5): ⇒ f(x)= 0

[214.5;260.5): ⇒ f(x)= 0

[260.5;306.5): 280 ⇒ f(x)= 1

Table and graphp attached.

I hope it helps!

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