Averages:
What is an average number and why do we need it? We will define an average number as a number, which is representative in value of a certain set of numbers and is calculated by the adding of all the numbers in that set and then by dividing by how many numbers there are.
Why do we need this concept? Very often, we need to refer to a number, which will represent a certain set of values and it is not practical or possible to express each individual value on its own.
For example, say that the month of July has been extremely hot and meteorologists need to compare the temperatures recorded during that month to wither other months of the year or to the months of July in previous years. They will likely find the average of the high temperatures during the month of that July by recording the high temperatures on each single day in that July and then by dividing by 31, since the month of July has 31 days.
Another practical and relevant example is an average mark. You will get a mark for each subject you are enrolled in. By adding all the individual marks and then by dividing by the number of subjects, whose marks you have added, you will arrive at your average mark.
The concept of average numbers is used very frequently in everyday life and though there is nothing complicated about it, we are including in our list of topics as a useful exercise.
There may be one hint we will share with you, that will help you in problems you may encounter in the future.
You may be asked to calculate the “missing mark”. You are told that the average of five marks is 70. You know four of the five marks. Can you think of how to figure out the remaining mark?
Stop at this point and try to get the answer on your own. If you cannot, below you will find the solution.
We know that we calculate the average by adding the five marks and then by dividing the total by 5. But in this case, we don’t have all 5 marks, only 4. However, we know the average and we know that 5 times the average must equal the total of the 5 marks. Therefore, if we multiply the average by 5 and subtract from that the total of the 5 numbers we have, that will give us the missing mark. We will demonstrate this concept for you in practical examples.
Examples:
1) |
Average of: 10, 11, 13, 16 |
|
11) |
Average of: 98, 99, 102, 104.6, 97 |
2) |
Average of: 9, 15, 16, 19, 25 |
|
12) |
Average of: 88, 104, 92, 79.6, 103.8 |
3) |
Average of: 62, 63, 68, 56, 59 |
|
13) |
Average of: 58, 47.9, 49.3, 51, 50.6 |
4) |
Average of: 13.6, 14.9, 12.8, 9.6 |
|
14) |
Average of: 228, 196, 199, 201, 214 |
5) |
Average of: 30, 27.6, 35.4, 42.8 |
|
15) |
Average of: 649, 599, 525, 617, 580 |
6) |
Average of: 112, 108, 120, 116, 114 |
|
16) |
Average of: -10, +2, -4, +6 |
7) |
Average of: 51, 48.6, 45, 49, 52.8 |
|
17) |
Average of: -16, -14, -19, -8 |
8) |
Average of: 96, 92, 94.8, 99, 101.2 |
|
18) |
Average of: 13.6, 27.2, 8.9, 20.4, 17.5 |
9) |
Average of: -12.6, -14.8, -16, -9.2 |
|
19) |
Average of: 249, 265.6, 237.9, 229.7 |
10) |
Average of: 15.1, 24.9, 9.5, 12.4, 17.6 |
|
20) |
Average of: 724, 689, 701.8, 704, 697 |
Answers:
1) |
12.5 |
|
11) |
100.12 |
2) |
16.8 |
|
12) |
93.48 |
3) |
61.6 |
|
13) |
51.36 |
4) |
12.725 |
|
14) |
207.6 |
5) |
33.95 |
|
15) |
594 |
6) |
114 |
|
16) |
-1.5 |
7) |
49.28 |
|
17) |
-14.25 |
8) |
96.6 |
|
18) |
17.25 |
9) |
-13.15 |
|
19) |
245.55 |
10) |
15.9 |
|
20) |
703.16 |
|
