# All about Averages

Hi, and welcome to this video on **Averages**! Today we will discuss:

- What an average is, and
- How you find the average of a set of data

Let’s start with the definition of an average. An average is the middle value of a set of numbers. Averages are used in a lot of areas of life, but the way you will most likely see it is in finding your final grade for the semester.

Thankfully for something so useful, it is fairly simple to figure out. The average of a set of data is found by taking the sum of all the values of a set of numbers and dividing by the total number of values.

Let’s look at an example:

A math teacher gives a test to her ten students. After grading the tests, she records the following scores: 100, 97, 65, 83, 77, 83, 72, 93, 81, and 99. What is the average score on this test?

Remember, the average is found by adding all the scores up and then dividing by the total number of students. So our first step is to add all our scores up.

\(100 + 97 + 65 + 83 + 77 + 93 + 81 + 72 + 83 + 99 = 850\)Then, we divide 850 by the total number of students, which is ten.

\(850\div 10=85\)So the average score on the test is 85.

Now, I want you to try one on your own. Here’s the problem:

Jonathan times his commute to school for five days. His times in minutes are: 7, 12, 13, 14, and 9. How long on average does it take him to commute to school?

Pause this video and try to solve this on your own. Once you have your answer, press play and see if your answer matches up with mine.

The first step in finding our average is to add all of our values together.

\(7 + 12 + 14 + 13 + 9 = 55\)Then we divide by the total number of values.

\(55\div 5=11\)So the average time it took him to commute to school is 11 minutes.

Before we go, let’s look at one more way averages are commonly used. You can use an average to find a missing value in your data set. The way you do this is by working in reverse of how we originally found the average. The first step is to take your average and multiply it by the number of values you have. Don’t forget to include the one that you’re looking for when you count! Then, we will subtract the values we know, and we will be left with our missing value. Let’s look at how to use this in real life:

Sarah wants to get a 90 for her quiz average in her math class for the semester. Her current quiz grades are: 88, 97, 86, and 92. What grade does she need to make on her last quiz to have a 90 average?

First, we are going to multiply her desired average, 90, by the total number of values. We are given four grades and know she has one more quiz, so our total number of values is 5.

\(90\cdot 5=450\)Now, all we do is subtract the values we already know from 450.

\(450 – 88 – 97 – 86 – 92 = 87\)She would need to get an 87 on her next quiz to have an average quiz score of 90.

And that’s all there is to it! Remember, to find the average, all you have to do is add all your numbers together and then divide by however many numbers you have. If you want to find a missing number and you are given the average, simply work backwards. Multiply your average by the amount of numbers you have, including the one you are looking for, and subtract the values you already know.

I hope this video helped you better understand how to use averages. Thanks for watching and happy studying!

## Practice Questions

**Question #1:**

It snows 13 inches on Monday, 5 inches on Tuesday, 12 inches on Wednesday, and 9 inches on Thursday. How many inches did it snow on Friday if the weekly 5-day snow average is 8 inches?

1 inch

5 inches

6 inches

9 inches

**Answer:**

To find the average snow accumulation for five days, the snow accumulation for all the days is added and divided by 5, which would result in 8 inches. We can use this information to set up an equation to help us find the value of the snow accumulation for Friday.

\(\frac{13+5+12+9+x}{5}=8\)

\(\frac{39+x}{5}=8\)

\(39+x=40\)

\(x=1\)

Therefore, the snow accumulation for Friday is 1 inch.

**Question #2:**

Kate’s weekly grocery bill for the last 7 weeks is $53.63, $74.89, $67.93, $77.03, $49.37, $58.33, and $65.25. How much does Kate spend on average at the grocery store per week?

$62.77

$63.78

$87.89

$89.29

**Answer:**

Kate’s average weekly grocery store spending can be calculated by adding the total weekly spending and dividing it by 7, since we have 7 weeks of weekly spending.

\(\frac{53.63+74.89+67.93+77.03+49.37+58.33+65.25}{7}\)

\(\frac{446.43}{7}≈63.78\)

Therefore, Kate spends $63.78 on average at the grocery store per week.

**Question #3:**

It takes Peyton 5 minutes to drive to work on Monday, 8 minutes on Tuesday, 7 minutes on Wednesday, 8 minutes on Thursday, 7 minutes on Friday, 10 minutes on Saturday, and 12 minutes on Sunday. On average, how long does it take Peyton to drive to work?

7.00 minutes

8.00 minutes

8.14 minutes

11.20 minutes

**Answer:**

We will add the daily times it takes Peyton to drive to work. Since we have data for 7 days, we will divide the total by 7 to find the average.

\(\frac{5+8+7+8+7+10+12}{7}\)

\(\frac{57}{7}≈8.14\)

Therefore, on average, it takes Peyton 8.14 minutes to drive to work.

**Question #4:**

The table shows Mona’s monthly electricity bill for one year.

January | $98.00 | July | $52.00 |

February | $105.00 | August | $47.00 |

March | $72.00 | September | $71.00 |

April | $66.00 | October | $85.00 |

May | $69.00 | November | $91.00 |

June | $54.00 | December | $105.00 |

What is Mona’s average monthly electric bill?

$71.50

$72.00

$76.25

$105.00

**Answer:**

To find Mona’s average monthly electric bill we will add the monthly bills and divide by 12, since there are 12 months in the year.

\(\frac{98+105+72+66+69+54+52+47+71+85+91+105}{12}\)

\(\frac{915}{12}=76.25\)

Therefore, Mona’s average annual electric bill is $76.25.

**Question #5:**

The table shows a player’s assists in the last 8 games.

Game 1 | 15 | Game 5 | 10 |

Game 2 | 12 | Game 6 | x |

Game 3 | 11 | Game 7 | 9 |

Game 4 | 11 | Game 8 | 7 |

If his 8-game assist average is 11, how many assists did he have in Game 6?

8

9

11

13

**Answer:**

The average of the player’s assists can be calculated by adding the assists for the 8 games and dividing by 8, which should equal 11 since that is the 8-game assist average. We can use this information to create an equation to solve for our unknown, the number of assists for Game 6.

\(\frac{15+12+11+11+10+9+7+x}{8}=11\)

\(\frac{75+ x}{8}=11\)

\(75+x=88\)

\(x=13\)

Therefore, the player had 13 assists in Game 6.