Is obtained by adding all the numbers in the set and dividing the sum by the number of values in that set?

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 [latex]85,88,\text{and }94[/latex]. To find the mean score, he would add them and divide by [latex]3[/latex].

[latex]\begin{array}{}\\ {\Large\frac{85+88+94}{3}}=\\ {\Large\frac{267}{3}}=\\ 89\end{array}[/latex]

His mean test score is [latex]89[/latex] points.

The Mean

The mean of a set of [latex]n[/latex] numbers is the arithmetic average of the numbers.

[latex]\text{mean}={\Large\frac{\text{sum of values in data set}}{n}}[/latex]

Calculate the mean of a set of numbers.

1. Write the formula for the mean
   [latex]\text{mean}={\Large\frac{\text{sum of values in data set}}{n}}[/latex]
2. Find the sum of all the values in the set. Write the sum in the numerator.
3. Count the number, [latex]n[/latex], 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 [latex]8,12,15,9,\text{ and }6[/latex].

Solution

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example

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

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Did you notice that in the last example, while all the numbers were whole numbers, the mean was [latex]59.5[/latex], 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 [latex]\text{\$42.75},\text{\$50.12},\text{\$41.54},\text{\$48.15}[/latex]. Find the mean cost of Daisy’s cell phone bills.

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In the next video we show an example of how to find the mean of a set of test scores.

The Mean of a Data Set

The mean of a set of numbers, sometimes simply called the average , is the sum of the data divided by the total number of data.

Example 1 :

Find the mean of the set { 2 , 5 , 5 , 6 , 8 , 8 , 9 , 11 } .

There are 8 numbers in the set. Add them all, and then divide by 8 .

2 + 5 + 5 + 6 + 8 + 8 + 9 + 11 8 = 54 8 = 6.75

So, the mean is 6.75 .

The Median of a Data Set

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

Example 1 :

Find the median of the set { 2 , 5 , 8 , 11 , 16 , 21 , 30 } .

There are 7 numbers in the set, and they are arranged in ascending order.  The middle number (the 4 th one in the list) is 11 .  So, the median is 11 .

Example 2 :

Find the median of the set { 3 , 10 , 36 , 255 , 79 , 24 , 5 , 8 } .

First, arrange the numbers in ascending order.

{ 3 , 5 , 8 , 10 , 24 , 36 , 79 , 255 }

There are 8 numbers in the set -- an even number. So, find the average of the middle two numbers, 10 and 24 .

10 + 24 2 = 34 2 = 17

So, the median is 17 .

The Mode of a Data Set

The mode of a set of numbers is the number which occurs most often.

Example 1 :

Find the mode of the set { 2 , 3 , 5 , 5 , 7 , 9 , 9 , 9 , 10 , 12 } .

2 , 3 , 7 , 10 and 12 each occur once.

5 occurs twice and 9 occurs three times.

So, 9 is the mode.

Example 2 :

Find the mode of the set { 2 , 5 , 5 , 6 , 8 , 8 , 9 , 11 } .

In this case, there are two modes -- 5 and 8 both occur twice, whereas the other numbers only occur once.

What is the sum of the numbers in set divided by the number of numbers?

What is it that takes the sum of all the numbers in a data set divided by the number of data points?

Can be obtained when you add up all the values in the given set and dividing it by the number of observations?

What measure of central tendency is used when adding all the values and dividing the sum by the number of values Brainly?