Mean

\bf\displaystyle Mean=\frac{Sum}{Count}


Basics

The term mean is synonymous with the term average.

The formula provided for mean by the Mathematics Formula Sheet is not presented as a mathematical expression.


Formulas (provided by Mathematics Formula Sheet)

Mean is equal to the total of the values of a data set, divided by the number of elements in the data set.

 

Formulas (NOT provided by Mathematics Formula Sheet)
\bf\displaystyle Mean=\frac{Sum}{Count}

\bf\displaystyle Sum = Mean\times\displaystyle Count

\bf\displaystyle Count=\frac{Sum}{Mean}

Sum = addition of values

Count = number of values


Question
Three people weigh 170, 186, and 244 pounds, respectively.  What is their mean weight?

Answer
200 pounds

Answer Process
Sum = addition of values = 170 + 186 + 244
Count = number of values = 3

\bf\displaystyle Mean=\frac{Sum}{Count}

Mean = \bf\displaystyle \frac{170 + 186 + 244}{3} = 200

Calculator Click What You See Comment
clear blinker clears screen
fraction 170+186+244
down 3 right
\bf\displaystyle\frac{170+186+244}{3} \bf\displaystyle Mean=\frac{Sum}{Count}
enter 200 Answer
Mean


Question
Five people weigh 120, 150, 170, 186, and 244 pounds, respectively.  What is their average weight?

Answer
174 pounds

Answer Process
Average is the same as Mean.

Sum = addition of values = 120 + 150 + 170 + 186 + 244
Count = number of values = 5

\bf\displaystyle Mean=\frac{Sum}{Count}

Mean = \bf\displaystyle \frac{120 + 150 + 170 + 186 + 244}{5} = 174

Calculator Click What You See Comment
clear blinker clears screen
fraction 120+150+170+186+244
down 3 right
\bf\displaystyle\frac{120+150+170+186+244}{5} \bf\displaystyle Mean=\frac{Sum}{Count}
enter 174 Answer
Mean


Question

The mean weight of four people is 165 pounds.  What is their total weight?

Answer
660 pounds

Answer Process
\bf\displaystyle Sum = Mean\times\displaystyle Count
Sum = 165 × 4 = 660

Calculator Click What You See Comment
clear blinker clears screen
165 × 4 165*4 \bf\displaystyle Sum = Mean\times\displaystyle Count
enter 660 Answer
Mean


Question

A group of people with a mean weight of 135 pounds weigh a total of 945 pounds.
How many people are in the group?

Answer
7

Answer Process
\bf\displaystyle Count=\frac{Sum}{Mean}

Count = \bf\displaystyle \frac{945}{135} = 7

Calculator Click What You See Comment
clear blinker clears screen
fraction 945
down 135 right
\bf\displaystyle\frac{945}{135} \bf\displaystyle Count=\frac{Sum}{Mean}
enter 7 Answer
Mean


Question

Three people have a mean weight of 145 pounds.  One person weighs 132 pounds.
A second person weighs 186 pounds.  What does the third person weigh?

Answer
117 pounds

Answer Process
Sum = Mean × Count
Sum = Mean × Count = 145 × 3 = 435

Unknown Value = Sum – Known Values
Unknown Value = 435 – 132 – 186 = 117

Calculator Click What You See Comment
clear blinker clears screen
145 × 3 145*3 \bf\displaystyle Sum = Mean\times\displaystyle Count
enter 435 Sum
435 – 132 – 186 435-132-186 Unknown Value =
Sum – Known Values
 enter 117 Answer
Mean


Practice – Questions
1.  Five basketball players scored 7, 12, 15, 28, and 33 points, respectively.  What was their mean score?

2.  Five basketball players scored 3, 6, 11, 18, and 47 points, respectively.  What was their average score?

3.  The mean bowling score of 8 people was 133.  What was their total score?

4.  A group of bowlers with a mean score of 147 had a total of score of 1617.  How many bowlers were in the group?

5.  Four bowlers had a mean score of 168.  One bowler scored 111.  A second bowler scored 133.  A third bowler scored 223.  What did the fourth bowler score?


Practice – Answers
1.  19

2.  17

3.  1064

4.  11

5.  205

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