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מדריכי לימוד > Prealgebra

Calculating the Mean of a Set of Numbers

Learning Outcomes

  • Find the mean of a set of numbers
 

The mean is often called the arithmetic average. It is computed by dividing the sum of the values by the number of values. Students want to know the mean of their test scores. Climatologists report that the mean temperature has, or has not, changed. City planners are interested in the mean household size. Suppose Ethan’s first three test scores were 85,88,and 9485,88,\text{and }94. To find the mean score, he would add them and divide by 33.

85+88+943267389\begin{array}{}\\ \frac{85+88+94}{3}\\ \frac{267}{3}\\ 89\end{array} His mean test score is 8989 points.

The Mean

The mean of a set of nn numbers is the arithmetic average of the numbers. mean=sum of values in data setn\text{mean}=\frac{\text{sum of values in data set}}{n}
 

Calculate the mean of a set of numbers.

  1. Write the formula for the mean mean=sum of values in data setn\text{mean}=\frac{\text{sum of values in data set}}{n}
  2. Find the sum of all the values in the set. Write the sum in the numerator.
  3. Count the number, nn, of values in the set. Write this number in the denominator.
  4. Simplify the fraction.
  5. Check to see that the mean is reasonable. It should be greater than the least number and less than the greatest number in the set.
 

example

Find the mean of the numbers 8,12,15,9,and 68,12,15,9,\text{and }6. Solution
Write the formula for the mean: mean=sum of all the numbersn\text{mean}=\frac{\text{sum of all the numbers}}{n}
Write the sum of the numbers in the numerator. mean=8+12+15+9+6n\text{mean}=\frac{8+12+15+9+6}{n}
Count how many numbers are in the set. There are 55 numbers in the set, so n=5n=5 . mean=8+12+15+9+65\text{mean}=\frac{8+12+15+9+6}{5}
Add the numbers in the numerator. mean=505\text{mean}=\frac{50}{5}
Then divide. mean=10\text{mean}=10
Check to see that the mean is 'typical': 1010 is neither less than 66 nor greater than 1515. The mean is 1010.
 
 

try it

[ohm_question]146388[/ohm_question]
 

example

The ages of the members of a family who got together for a birthday celebration were 16,26,53,56,65,70,93,and 9716,26,53,56,65,70,93,\text{and }97 years. Find the mean age.

Answer: Solution

Write the formula for the mean: mean=sum of all the numbersn\text{mean}=\frac{\text{sum of all the numbers}}{n}
Write the sum of the numbers in the numerator. mean=16+26+53+56+65+70+93+97n\text{mean}=\frac{16+26+53+56+65+70+93+97}{n}
Count how many numbers are in the set. Call this nn and write it in the denominator. mean=16+26+53+56+65+70+93+978\text{mean}=\frac{16+26+53+56+65+70+93+97}{8}
Simplify the fraction. mean=4768\text{mean}=\frac{476}{8}
mean=59.5\text{mean}=59.5
Is 59.559.5 ‘typical’? Yes, it is neither less than 1616 nor greater than 9797. The mean age is 59.559.5 years.

 

try it

[ohm_question]146389[/ohm_question]
  Did you notice that in the last example, while all the numbers were whole numbers, the mean was 59.559.5, a number with one decimal place? It is customary to report the mean to one more decimal place than the original numbers. In the next example, all the numbers represent money, and it will make sense to report the mean in dollars and cents.  

example

For the past four months, Daisy’s cell phone bills were $42.75,$50.12,$41.54,$48.15\text{\$42.75},\text{\$50.12},\text{\$41.54},\text{\$48.15}. Find the mean cost of Daisy’s cell phone bills.

Answer: Solution

Write the formula for the mean. mean=sum of all the numbersn\text{mean}=\frac{\text{sum of all the numbers}}{n}
Count how many numbers are in the set. Call this nn and write it in the denominator. mean=sum of all the numbers4\text{mean}=\frac{\text{sum of all the numbers}}{4}
Write the sum of all the numbers in the numerator. mean=42.75+50.12+41.54+48.154\text{mean}=\frac{42.75+50.12+41.54+48.15}{4}
Simplify the fraction. mean=182.564\text{mean}=\frac{182.56}{4}
mean=45.64\text{mean}=45.64
Does $45.64\text{\$45.64} seem ‘typical’ of this set of numbers? Yes, it is neither less than $41.54\text{\$41.54} nor greater than $50.12\text{\$50.12}. The mean cost of her cell phone bill was $45.64\text{\$45.64}

   

TRY IT

[ohm_question]146394[/ohm_question] [ohm_question]146390[/ohm_question]
In the next video we show an example of how to find the mean of a set of test scores. https://youtu.be/0io9U8Jcjeo  

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