Answers to Last Week’s exercises Hello boys and girls,

Welcome to this week’s Mathematics Corner. Last week, we examined various concepts of a circle, including the calculation of its circumference, diameter and radius. In this week’s column, we’ll move on to a new topic. We will be examining the concept of mode, mean/average and median.

Let’s begin. Mean, median, and mode

Mean, median, and mode are different measures of centre in a numerical data set. They each try to summarize a dataset with a single number to represent a “typical” data point from the dataset.

Let’s examine the concept of the mode.

Mode

What is the mode?

The mode is the most frequent number—that is, the number that occurs the highest number of times.

Example 1: The mode of {4, 2, 4, 3, 2, 2} is which is more than any other number.

Work the exercise below:

Exercise 1

Identify the mode in each of the following: 2,2,5,7,6,7,4,2 1,2,3,4,5,6,4,7 7,6,5,7,8,9,7,3 0,1,4,3,2,2,3,3 5,5,6,7,7,8,3,3,5,5

Mean/Average

Example 1

Formula: Mean/Average = = 8 + 9 + 5 + 6 + 7 = 35 = 35/5 = 7

Mean= 7

Exercise 2 2

because ‘2’ occurs three times,

Great job, boys and girls! Wasn’t that a very simple exercise? Yes, it was!

Let’s now take a look at what the Mean/Average entails.

The mean is the average of a data set, found by adding all the numbers together, and then dividing the sum of the numbers by the number of numbers.

Find the average of the data set: {8, 9, 5, 6, 7}

Sum of terms Number of terms

Now, boys and girls, apply the knowledge you have learned by completing the exercise below: a) Calculate the mean of 43, 37 and 73. b) What is the mean of 30, 60 and 9? c) Sarah did 4 tests and made a total score of 824. What was her mean score?

d) Joy did 5 tests and obtained a total score of 100. What was her mean score?

e) Sandra scored 500 marks in 10 tests. What was her mean score?

Great work!

Now boys and girls, if we are given the total and the mean, and are asked to find the number of scores, what do you think we should do?

Let’s see if your assumption is correct.

Finding the number of scores, given the total and the mean

Formula:

Example 1:

Formula:

Exercise 3

Let’s find out!

Formula: Sum = Mean x Number of scores

Example 1

Exercise 4

Median

Sum Mean

The mean of a set of numbers is 6. The sum of the numbers is 18. How many numbers are there?

Sum Mean

= 18 = 3 (number of scores) 6

Complete the exercise below:

1. The mean of a set of numbers is 5. The numbers add up to 20. How many numbers are there?

2. The mean of a set of numbers is 10. The numbers add up to 100. How many numbers are there?

3. The mean of a set of numbers is 5. The numbers add up to 40. How many numbers are there?

4. If the mean of a set of numbers is 8, and its sum is 72, how many numbers are there?

5. What is the number of scores, if the mean of a set of scores is 12, while its total is 48?

Now boys and girls, what if we are given the mean and number of scores and are asked to calculate the sum? What should we do?

Calculating the total/Sum, given the mean and number of scores.

The mean of 4 scores is 12. What is the sum of the four scores?

Formula: Sum = Mean x Number of scores

The Median is the = 12 x 4 = 48 1. The mean of 5 numbers is 20. What is the sum of the five numbers?

2. If the average of 3 numbers is 20, what is the total of the three numbers?

3. Sarah’s average in in 5 tests is 40. What is the total of her five tests?

4. The mean of 6 numbers is 30. What is the sum of the six numbers? 5. The mean of 4 numbers is 32. What is the sum of the four numbers?

Let’s now examine the final concept for today. The Median!

What is the median? “middle” of a sorted list of numbers. In other words, it is