Data Handling II

Grade 10 Math - Data Handling

Lesson Objectives

Define and understand mean, median, and mode.
Calculate measures of central tendency from raw and grouped data.
Interpret and compare data using central tendency.
Apply knowledge to real-life and exam-based data questions.

Lesson Introduction

When we collect data, we often want to summarize it using a single number that best represents the whole data set. This is where the measures of central tendency come in. In this lesson, we will learn how to calculate the mean, median, and mode, and how to use them to interpret data in various situations.

Core Lesson Content

Mean: Also known as the average. It is calculated by dividing the sum of values by the number of values.

$\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}$

Median: This is the middle value when data is arranged in ascending or descending order. If the number of values is even, it is the average of the two middle values.

Mode: The number that appears most frequently in a data set. A data set may have one mode, more than one mode, or no mode at all.

Worked Example

Example 1: Calculate the mean of 5, 7, 9, 10, and 14.

\text{Mean} = \frac{5 + 7 + 9 + 10 + 14}{5} = \frac{45}{5} = 9

Example 2: Find the median of 4, 6, 8, 10, 12.
Data is already ordered. The middle value is

8

Example 3: Find the median of 3, 5, 7, 9.

\text{Median} = \frac{5 + 7}{2} = 6

Example 4: Find the mode of the data: 2, 4, 4, 5, 6.
Mode = 4 (since it appears most frequently).

Example 5: A student scored 55, 60, 60, 70, 75. What is the mean?

\text{Mean} = \frac{55 + 60 + 60 + 70 + 75}{5} = \frac{320}{5} = 64

Example 6: Calculate the mean of the data: 10, 20, 30, 40, 50, 60.

\text{Mean} = \frac{210}{6} = 35

Example 7: Find the mode of the data: 1, 3, 3, 4, 5, 6, 6, 6, 8.
Mode = 6

Example 8: Determine the median of the data: 14, 16, 17, 18, 20, 22, 24.
Median = 18

Example 9: Calculate the mean score of 5 students: 40, 50, 60, 70, 80.

\text{Mean} = \frac{40 + 50 + 60 + 70 + 80}{5} = \frac{300}{5} = 60

Example 10: Find the mean of the frequencies in the table:

Value (x)	Frequency (f)
2	1
4	2
6	3

\text{Mean} = \frac{(2 \times 1) + (4 \times 2) + (6 \times 3)}{1 + 2 + 3} = \frac{2 + 8 + 18}{6} = \frac{28}{6} = 4.67

Exercises

Find the mode in the set: $3, 5, 7, 5, 9, 5, 11$ .
[WAEC] Calculate the mean of the following data: $4, 8, 12, 16, 20$ . [Past Question]
Find the median of: $6, 8, 10, 12, 14, 16$ .
The median of the numbers $2, 3, 4, 6, 8, 9, 11$ is what?
[NECO] The marks scored by a student are: $72, 65, 80, 90, 85$ . Find the mean mark. [Past Question]
Determine the mode from this set: $4, 6, 6, 7, 8, 10$ .
[NABTEC] A frequency table is given: $x = 1, 2, 3$ ; $f = 2, 3, 5$ . Find the mean. [Past Question]
In a data set $10, 15, 15, 20, 25$ , calculate the mean, median, and mode.
[JAMB] The average height of 5 players is $1.8\, \text{m}$ . What is the total height? [Past Question]
What is the mode of the ages: $15, 16, 17, 15, 16, 18$ ?

Conclusion/Recap

In this lesson, we explored how to calculate and interpret the measures of central tendency: mean, median, and mode. These are essential tools for analyzing and summarizing data. In the next lesson, we will delve into measures of dispersion like range, variance, and standard deviation.