Question

Short Response Find the mean of these temperatures:$- {12}^0\text{F}, 7^0\text{F,} -{22}^0\text{F,} -{11}^0\text{F}, {20}^0\text{F,} - 6^0\text{F}$ Describe the steps you used.

Short answer

The mean of the temperature is – 4⁰F.

Step-by-step solution

Step-1 – What is the meaning mean of data set? 

In mathematics, the arithmetic average of a number of observations is called mean of the data set.

Step-2 – How to find the mean of a data set 

The mean is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.

How to Find the Mean

By adding all data values to get the sum, and then count the number of values in your data set. At last divide the sum by the count.

$\text{Mean}=\frac{\text{Sum of all observations}}{\text{count of observations}}$

Step-3 – Example for finding mean of a data set

The mean is the total of the numbers divided by how many numbers there are.

To find the mean, add all the numbers together then divide by the number of numbers.

Example: Say you’re given the following set of data:6, 10, 3, 27, 19, 2, 5, 14

To find the mean, you’ll first need to add up all the values in the data set like this:

6 + 10 + 3 + 27 + 19 + 2 + 5 +14 = 86

The last step is to take this sum (86) and divide it by the number of values in the data set.

There are eight different values (6, 10, 3, 27, 19, 2, 5, 14), we'll be dividing 86 by 8: $86 ÷ 8 = 10.75$

The mean, or average, for this set of data is 10.75.

 Find the mean of the data set: – 120F, 70F, – 220F, – 110F, 200F, – 60F, 

To find the mean, you’ll first need to add up all the values in the data set like this:

(– 12+ 7+ – 22+ – 11+, 20+ – 6 )⁰F = – 24⁰F

The last step is to take this sum (86) and divide it by the number of values in the data set.

Because there are eight different values (– 12⁰F, 7⁰F, – 22⁰F, – 11⁰F, 20⁰F, – 6⁰F), we'll be dividing – 24⁰F by 6.

Mean of the temperatures is:– 24⁰F ÷ 6 = – 4⁰F.