Bar Graphs and Histograms

Statistics: Data Collection and Graphs

Lesson Objectives

Understand methods of data collection and representation.
Interpret data using statistical graphs such as bar charts and histograms.

Lesson Introduction

Statistics involves collecting, organizing, analyzing, and interpreting numerical data. It helps in making informed decisions based on patterns and trends.

Examples: Collecting and Interpreting Data

Example 1:
A survey was conducted on the favorite sport of 30 students. The results were: Football (12), Basketball (8), Volleyball (6), Others (4). Represent the data in a frequency table.

Example 2:
From the following scores of students in a math test: 55, 60, 60, 65, 70, 70, 70, 75, 80, 85 — determine the mode.
Solution: The number that appears most is 70 ⇒ Mode = 70.

Example 3:
If the marks of 5 students are 45, 50, 55, 60, and 65, calculate the mean.
Mean = \( \frac{45 + 50 + 55 + 60 + 65}{5} = \frac{275}{5} = 55 \)

Example 4:
Given the frequency table below, determine the total number of students.

Grade	Frequency
A	5
B	10
C	8
D	7

Total = \( 5 + 10 + 8 + 7 = 30 \)

Example 5:
[NECO] A class of 40 students recorded the following number of absentees over 5 days: 2, 3, 5, 4, 6. Find the average number of absentees per day. (Past Question)
Mean = \( \frac{2 + 3 + 5 + 4 + 6}{5} = \frac{20}{5} = 4 \)

Examples: Constructing Bar Charts and Histograms

Example 6:
Construct a bar chart to represent the data: Apples (20), Bananas (15), Oranges (10), Mangoes (5).

Example 7:
Given the frequency of marks scored in intervals: 0–10 (2), 11–20 (5), 21–30 (7), 31–40 (4), construct a histogram.

Example 8:
[WAEC] The number of books read by students in a month: 1 (3 students), 2 (5 students), 3 (6 students), 4 (2 students). Draw a bar chart. (Past Question)

Example 9:
Using the table below, construct a histogram.

Interval	Frequency
10–20	4
20–30	7
30–40	9

Example 10:
The ages of students in a class are grouped as: 10–12 (5), 13–15 (8), 16–18 (6). Construct a bar chart.

Exercises

Collect data on the number of siblings of your classmates and present in a frequency table.
Find the mode of the following data: 10, 15, 15, 20, 25, 25, 25, 30.
Calculate the mean of: 5, 10, 15, 20, 25.
[NECO] A class of 20 students scored: 5, 6, 7, 5, 6, 8, 9, 10, 5, 6. What is the mode? (Past Question)
Construct a bar chart for the number of cars in 5 families: 1 (3 families), 2 (5 families), 3 (2 families).
Given scores in intervals: 0–5 (2), 6–10 (3), 11–15 (6), draw a histogram.
From a class of 25, the students chose colors: Red (10), Blue (8), Green (7). Represent with a bar chart.
[WAEC] Construct a histogram for the intervals: 5–10 (4), 10–15 (6), 15–20 (3). (Past Question)
Calculate the average age if the ages of 4 students are: 12, 14, 16, 18.
Interpret the data from the histogram showing student attendance over 5 weeks.

Conclusion/Recap

Data can be collected using surveys or observations and represented using tables and charts. Bar charts are used for discrete data, while histograms represent continuous data. Interpreting data helps us find averages, trends, and make informed decisions.