CK-12-Basic Probability and Statistics Concepts - A Full Course

http://www.ck12.org Chapter 5. Measures of Central Tendency

For the population,N=25 and∑m f=545, so using the formulaμ=∑Nm f, the mean would again beμ=^54525 = 21 .8.

Example B

In Example A, suppose the distribution of driving times were broken down into smaller intervals as shown:

TABLE5.9:

Driving Times (minutes) Number of Teachers

0 to less than 5 2

5 to less than 10 1

10 to less than 15 4

15 to less than 20 6

20 to less than 25 3

25 to less than 30 3

30 to less than 35 1

35 to less than 40 3

40 to less than 45 1

45 to less than 50 1

Calculate the mean of the driving times.

First create the table below:

TABLE5.10:

Driving Times (minutes) Number of Teachersf Midpoint Of Classm Productm f

0 to less than 5 2 2.5 5.0

5 to less than 10 1 7.5 7.5

10 to less than 15 4 12.5 50.0

15 to less than 20 6 17.5 105.0

20 to less than 25 3 22.5 67.5

25 to less than 30 3 27.5 82.5

30 to less than 35 1 32.5 32.5

35 to less than 40 3 37.5 112.5

40 to less than 45 1 42.5 42.5

45 to less than 50 1 47.5 47.5

Now the mean can be calculated as shown:

μ=

∑m f

N

μ=

5. 0 + 7. 5 + 50. 0 + 105. 0 + 67. 5 + 82. 5 + 32. 5 + 112. 5 + 42. 5 + 47. 5

25

μ=

552. 5

25

μ= 22. 1

This time, the mean time spent by each teacher driving from home to school is 22.1 minutes. Thus, the mean for
grouped data can change based on the size of the intervals.