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

5.3. Grouped Data to Find the Mean http://www.ck12.org

Calculate the mean number of hours per week spent by each student texting messages on a cell phone. Hint: A table
may be useful.

Answer:

First create the table below.

TABLE5.14:

Time Per Week (Hours) Number of Studentsf Midpoint of Classm Productm f

0 to less than 5 8 2.5 20.0

5 to less than 10 11 7.5 82.5

10 to less than 15 15 12.5 187.5

15 to less than 20 12 17.5 210.0

20 to less than 25 9 22.5 202.5

25 to less than 30 5 27.5 137.5

Now that you have created several distribution tables for grouped data, it’s time to point out that the first column of
the table can be represented in another way. As an alternative to writing the interval, or class, in words, the words
can be expressed as [# - #), where the front square bracket closes the class, so the first number is included in the
designated interval, but the open bracket at the end does not close the class, so the last number is not included in the
designated interval. Keeping this in mind, the table above can be presented as follows:

TABLE5.15:

Time Per Week (Hours) Number of Studentsf Midpoint of Classm Productm f

[ 0 − 5 ) 8 2.5 20.0

[ 5 − 10 ) 11 7.5 82.5

[ 10 − 15 ) 15 12.5 187.5

[ 15 − 20 ) 12 17.5 210.0

[ 20 − 25 ) 9 22.5 202.5

[ 25 − 30 ) 5 27.5 137.5

Now the mean can be calculated as shown:

x=

∑m f

n

x=

20. 0 + 82. 5 + 187. 5 + 210. 0 + 202. 5 + 137. 5

60

x=

840

60

x= 14

The mean time spent per week by each student texting messages on a cell phone is 14 hours.

Practice

1. Match the words in the left column with the correct symbol from the right column.