CK-12 Basic Probability and Statistics - A Short Course

6.1. The Mean http://www.ck12.org

x ̄=

∑x 1 f 1 +x 2 f 2 +x 3 f 3 +...+xnfn

f 1 +f 2 +f 3 +...+fn

x ̄=

612 + 714 ( 3 )+ 712 ( 8 )+ 734 ( 10 )+ 814 ( 7 )+ 812 ( 4 )+ 914 ( 2 )

1 + 3 + 8 + 10 + 7 + 4 + 2

x ̄=

276

35

x ̄= 7

31

35

≈ 7. 89

The mean hand span for the 35 students is approximately 7.89 inches.

Lesson Summary

You have learned the significance of the mean as it applies to a set of numerical data. You have also learned how to
calculate the mean when the data is presented as a list of numbers as well as when it is represented in a frequency
table. To facilitate the process of calculating the mean, you have also learned to apply the formulas necessary to do
the calculations.

Points to Consider

• Is the mean only important as a measure of central tendency?


• If data is represented in another way, is it possible to either calculate or estimate the mean from this other
  representation?

Review Questions

1. Find the mean of each of the following sets of numbers:
   a. 3, 5, 5, 7, 4, 8, 6, 2, 5, 9
   b. 8, 3, 2, 0, 4, 3, 4, 6, 7, 9, 5
   c. 3, 8, 4, 1, 8, 7, 5, 6, 3, 7, 2, 9
   d. 18, 28, 27, 27, 23, 22, 25, 21, 1


2. The number of days it rained during four months were: April –11 days May –8 days June –13 days July –24
   days Find the mean number of rainy days per month.


3. Busy Bobby earned the following amounts of money over a four week period: Week One - $106.64 Week
   Two - $120.42 Week Three - $110.54 Week Four - $122.16 Find the mean weekly wage.


4. Mary Hop must ride to her workplace on the bus. She found that the number of minutes she spent riding on
   the bus each day was different.|Following are the number of minutes she recorded for the five work days last
   week: Monday –43 minutes Tuesday –50 minutes Wednesday –47 minutes Thursday –49 minutes Friday –41
   minutes How many minutes are there in the mean trip?


5. The number of fans that attended the last six games of the local baseball team during the cup competition
   were:

5200 , 8130 , 11250 , 13208 , 18750 , 24060

What was the mean attendance for each game?

6. Two dice were thrown together six times and the results are shown below: First Throw –3 Second Throw –7
   Third Throw –11 Fourth Throw –9 Fifth Throw –12 Sixth Throw –6 What is the mean of these throws of the
   dice?


7. The frequency table below shows the number of Tails when four coins are tossed 64 times. What is the mean?