Statistics of Frequency Distributions

This is the interval between two consecutive upper (or lower) class limits.

• class width

• class boundaries

• midpoints

• frequency

These are used as the border between two consecutive bars in a histogram. They are the intermediate value between an upper class limit and the next lower class limit.

• class limits

• class boundaries

• frequencies

• class marks

How do you calculate the class width if you have a data set of 70 entries and you are asked to construct a 6 class frequency distribution?

• I divide 70/6=11.66666, I round it up to 12; the class width is 12.

• I divide 6/70=0.875, I round it up to 9; the class width is 9.

• I choose a class width of 10 because it looks fine.

• As there are 70 entries, each class width is 6.

Why is this frequency distribution incorrect?

• The fourth class width is different from the others

• There is a zero.

• Classes should overlapped.

Find the midpoints.

• 25.5, 35.5, 45.5, 55.5, 65.5, 75.5

• 20.5, 30.5, 40.5, 50.5, 60.5, 70.5, 80.5

• 21, 31, 41, 51, 61, 71

• 30, 40, 50, 60, 70, 80

Find the relative frequencies

• 37%, 76%, 92%, 95%, 98%, 100%

• 28%, 30%, 12%, 2%, 2%, 2%

• 33%, 37%, 20%, 7%, 7%, 7%

• 37%, 39%, 16%, 3%, 3%, 3%

Find the cumulative frequencies.

• 28, 56, 84, 100

• 28, 58, 70, 72, 74, 76

• 33%, 37%, 20%, 7%, 7%, 7%

• 28, 30, 12, 2, 2, 2

Look at the frequency distribution. Find the class boundaries.

• 21, 31, 41, 51, 61, 70, 80

• 25.5, 35.5, 45.5, 55.5, 65.5, 75.5

• 20.5, 30.5, 40.5, 50.5, 60.5, 70.5

• 30, 40, 50, 60, 70, 80

What type of distribution is this?

• Normal
• Symmetric
• Positively Skewed
• Negatively Skewed

Which interval has 400 employees?

• 33-43
• 0-10
• 77-87
• 66-76