Everyday Statistics – Pictogram, Bar Chart and Pie Chart | Measure of Central Tendency – Mode, Median, Mean and Range | Probability Primary 6 (Basic 6) Term 3 Week 6 Mathematics

 

MATHEMATICS 

THIRD TERM

WEEK 6

PRIMARY 6

THEME –  DATA COLLECTION AND PRESENTATION 

PREVIOUS LESSON – Volume and Capacity of Three Dimensional Shapes – Cube, Cuboid, Prism, Cylinder, Cone, etc. Primary 6 (Basic 6) Term 3 Week 5 Mathematics

 

TOPIC – EVERYDAY STATISTICS 

 

LEARNING AREA

1. Introduction

2. Data Collection and Presentation

3. Range and Measures of Central Tendency

4. Probability

5. Lesson Evaluation and Weekly Assessment (Test)

 

 

LEARNING OBJECTIVES 

By the end of the lesson, most pupils should have attained the following objectives –

 

1. interpret pictograms and bar graphs.

2. use pictograms and bar graphs in representing population of people or data.

3. read tally marks and frequency tables.

4. interpret and draw pie charts.

5. calculate range and measures of central tendency.

 

 

ENTRY BEHAVIOUR

The pupils can count and compare the number of boys and girls in the class.

 

 

INSTRUCTIONAL MATERIALS

The teacher will teach the lesson with the aid of:

 

1. class population.

2. chart showing frequency tables, pictogram, pie chart and bar chart.

3. Graph sheet of papers

 

 

METHOD OF TEACHING

Choose a suitable and appropriate methods for the lessons.

Note – Irrespective of choosing methods of teaching, always introduce an activities that will arouse pupil’s interest or lead them to the lessons. 

 

 

REFERENCE MATERIALS

1. Scheme of Work

2. 9 – Years Basic Education Curriculum

3. Course Book

4. All Relevant Material

5. Online Information

 

 

CONTENT OF THE LESSON  

LESSON 1 – INTRODUCTION 

ACTIVITY 1 – DATA COLLECTION AND PRESENTATION (5 minutes) 

Teacher organizes pupils in groups or pairs depending on the size of the class and leads them to,

• count and record the number of boys and girls in the school.

• present the data collected in a simple table and chart.

 

RECORDS               BOYS                   GIRLS

Primary 1                    12                        19

Primary 2                      7                        11

Primary 3                    17                        14

Primary 4                      9                        21

Primary 5                    12                        19

Primary 6                      9                        12

 

MEANING OF DATA COLLECTION

Data collection is the gathering of facts and figures needed for the research purposes.

 

MEANING DATA PRESENTATION 

Data presentation is the process of using different graphical formats to represent the relationship between two or more data to important decisions.

 

ACTIVITY 2 – TALLY AND FREQUENCY TABLE (5 minutes) 

RECORDS               BOYS                  GIRLS

Primary 1                //// //// //                //// //// ////

Primary 2                //// //                     //// //// /

Primary 3                //// //// //// //          //// //// ////

Primary 4                //// ////                   //// //// //// //// /

Primary 5                //// //// //                //// //// ////

Primary 6                //// ////                    //// //// //

Note – / = 1,    //// = 5

 

ACTIVITY 4 – PICTOGRAM AND BAR CHART (5 minutes) 

A pictogram is a chart or graph that uses represent data with pictures.

For example,

 

COLOURS 

RED                      ❤️❤️❤️❤️❤️❤️❤️

GREEN                 💚💚💚💚💚

YELLOW              💛💛💛💛💛💛💛💛💛

BLUE                    💙💙💙💙💙💙💙💙

KEY – ❤️ = 1 💚 = 2 💛 = 1 💙 = 1

 

1. How many red colours?

2. How many yellow colours?

3. How many blue colours?

4. How many green colours?

5. What the sum of all the colours?

 

WORKING

Given, ❤️ = 1 💚 = 2 💛 = 1 💙 = 1

1. Red colour is 7.

2. Yellow colour is 9.

3. Blue colour is 8.

4. Green colour is 10.

5. Total colour is 7 + 9 + 8 + 10 = 34

 

ACTIVITY 5 – BAR CHART 

A bar chart is a graph that represents data using rectangular bars.

 

For example,

FAVOURABLE COLOURS 

 

1. How many red colours?

2. How many yellow colours?

3. How many blue colours?

4. How many green colours?

5. How many pink colours?

6. What the sum of all the colours?

 

WORKING

1. Red colour is 8.

2. Yellow colour is 7.

3. Blue colour is 5.

4. Green colour is 9.

5. Pink colour is 6.

6. 8 + 7 + 5 + 9 + 6 = 35

 

WORKING EXERCISE 

1. Number of Children Absent in School

Monday            🧓🧓🧓🧓

Tuesday            🧓🧓🧓🧓🧓🧓🧓

Wednesday      🧓🧓🧓🧓🧓🧓

Thursday          🧓🧓🧓🧓🧓🧓🧓🧓🧓🧓🧓🧓

Friday               🧓🧓🧓🧓🧓🧓🧓🧓🧓🧓

 

KEY – 🧓 = 2 children

• Which day has the least of children that were absent?

• Which day has the least of children that were absent?

• What is the title of the graph?

• How many children were absent on Thursday?

• Which day has the least of children that were absent?

• Which day has the most of children that were absent?

• What total number of children absent for the week?

 

2. Mode of Transportation

 

• What type of chart is this?

• What is the least mode of transportation?

• What is the most mode of transportation?

• What is the total mode of transportation?

• What is different between most and least mode of transportation?

 

 

LESSON 2 – PIE CHART 

ACTIVITY 1 – INTRODUCTION 

A pie chart is a  chart that represents data in a graphical manner.

 

 

ACTIVITY 2 – INTERPRETATION OF PIE CHART 

 

 

 

LESSON 3 – RANGE AND MEASURES OF CENTRAL TENDENCY 

ACTIVITY 1 – RANGE 

Range is the difference between the largest and smallest data in a given set.

For example,

The number of children in all classes are as:

Primary 1 – 26

Primary 2 – 18

Primary 3 – 31

Primary 4 – 30

Primary 5 – 26

Primary 6 – 21

The range is the highest class – the lowest class.

That’s,

Range = 31 – 18 = 13 children

 

WORKING EXAMPLE 2 

 

Use the above chart to find the range of the mode of transportation.

The most mode of transportation is 35, while the least mode of transportation is 3.

Range is the different between 35 and 3.

That’s,

Range, 35 – 3 = 32

 

WORKING EXAMPLE 3

The ages of 10 children in a class are as follows:

11 years, 14 years, 8 years, 12 years, 14 years, 20 years, 15 years, 9 years, 16 years and 10 years.

The highest is 20 years.

The lowest is 8 years.

Range,

= 20 years – 8 years

= 12 years

 

ACTIVITY 3 – MEASURES OF CENTRAL TENDENCY

There are three (3) main measures of central tendency,

1. Mode

2. Median

3. Mean

Measures of central tendency are used to describe or summarize a set of data within a give set.

 

ACTIVITY 4 – MODE 

The mode is the most common number within a given set of data.

OR the number that appears most.

For example,

Find the mode of 8 6 8 9 7 7 5 10 6 5 6 6 6 7 8 8 9 10

5, 2 times

6, 5 times

7, 3 times

8, 4 times

9 2 times

10, 2 times

Since, 6 appears 5 times.

Therefore, the mode is 6.

 

ACTIVITY 5 – MEDIAN 

Median is the middle value in a set arranged from smallest to largest.

Median can be odd value or even value.

 

1. FINDING MEDIAN WITH AN ODD VALUE 

Find the median of the following set,

8 6 8 9 7 7 5 10 6 5 6 6 6 7 8 8 9

Step 1 – Write the numbers in order either ascending or descending.

2 2 6 6 6 6 6 7 7 7 8 8 8 8 9 9 10

Step 2 – Find the middle number.

2 2 6 6 6 6 6 7   7   7 8 8 8 8 9 9 10

The median of set data is 7.

 

2. FINDING MEDIAN WITH AN EVEN VALUE 

Find the median of the following set,

9 6 2 8 10 3 2 8 9 8 3 6 3 8 6 10 3 9

 

Step 1 – Write the numbers in order either ascending or descending.

10 10 9 9 9 8 8 8 8 6 6 6 3 3 3 3 3 3 3 3

 

Step 2 – Find the middle number.

10 10 9 9 9 8 8 8 8 6 6 6 3 3 3 3 3 3 3 3

The middle numbers are 8 and 6.

 

Step 3 – Add the two middles and divide by 2, the middle numbers are even numbers.

That’s,

8 + 6

  ________

2

= 14/2

= 7

The median of set data is 7.

 

WORKING EXERCISE (ASSIGNMENT) 

Find the range, mode and median of the following:

1. 9, 7, 11, 13, 7, 5, 7, 2, 4, 11, 5, 5, 5

2. 17, 18, 19, 21, 20, 23, 23, 27, 29, 29, 35

3. 8.3, 9.4, 8.1, 9.3, 8.2, 9.3, 8.4, 9.2, 9.1, 8.5, 9.4

 

LESSON 4 – MEAN

ACTIVITY 1 – INTRODUCTION 

Mean is the average or most common value used of the central measure of tendency.

Mean is an average.

An average is the sum of the data divided by the number of data count in a set.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

For example,

Find the mean of the following:

2, 4, 6, 8, 10 and 12

Step 1 – Add the set number together.

 2 + 4 + 6 + 8 + 10 + 12 = 42

Step 2 – Divide by the number of data.

42/6 = 7

The mean is 7.

 

WORKING EXAMPLE 2

The marks of 20 pupils in a class are 88, 82, 88, 85, 84, 80, 81, 82, 83, 85, 84, 74, 75, 76, 89, 90, 89, 80, 82, and 83.

Find the range, mode, median and mean of the scores.

 

SOLUTION

1. Range = highest score – lowest score

= 88 – 74

= 14

 

2. Mode

74, 75, 76, 80, 81, 82, 82, 82, 83, 83, 84, 84, 85, 85, 88, 88, 89, 89, 89, 90

82 appeared 3 times.

Therefore, the mode of the mark is 82.

 

3. Median

74, 75, 76, 80, 81, 82, 82, 82, 83, 83, 84, 84, 85, 85, 88, 88, 89, 89, 89, 90

The meddle values are even, 83 and 84.

Therefore,

83 + 84 = 167

167/2 = 83.5

The median mark is 83.5.

 

4. Mean

88 + 82 + 88 + 85 + 84 + 80 + 81 + 82 + 83 + 85 + 84 + 74 + 75 + 76 + 89 + 90 + 89 + 80 + 82 + 83 = 1660

= 1660/20

= 83

The mean of the mark is 83.

 

LESSON 5 – REVISION AND WEEKLY ASSESSMENT 

As stated in performance objectives or lesson evaluation. 

 

 

PRESENTATION

To deliver the lesson, the teacher adopts the following steps:

1. To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;

2. Teacher organizes the pupils in groups or pair depending on the size of the class.

3. Teacher leads the groups or pairs of collect the number of boys and girls in all the classes.

Pupil’s Activities – As groups or pairs, take record of boys and girls in all the classes.

4. Teacher guides pupils to represent the data collected on a simple tally table and chart.

Pupil’s Activities – Represent data on a simple tally table and chart.

5. Teacher appreciates the individual’s and groups or pairs active participation and uses the their activities to introduce the lesson.

Pupil’s Activities – Pay attention to the lesson introduction to understand the concept of the lesson.

6. Teacher displays pictogram and bar chart for the pupils to examine as groups or pairs.

7. Teacher leads pupils to analyze and interpret the data on the pictogram and bar chart.

8. Teacher guides pupils to correctly represent data on pictogram and chart chart.

Pupil’s Activities – Analyze, interpret and represent data on pictogram and chart chart.

9. Teacher guides to interpret and draw a pie chart.

10. Teacher leads pupils to solve questions on pie chart.

Pupil’s Activities – Solve questions on pie chart.

11. Teacher leads a discussion on measures of central tendency.

12. Teacher guides pupils to find range, mode, median and calculate mean of a given data.

Pupil’s Activities – Describe the range and measures of central tendency and solve related questions.

13. Teacher summarizes the lesson on the board with appropriate evaluation.

Pupil’s Activities – Participate actively in the summary of the lesson and write as instructed.

 

 

CONCLUSION

To conclude the lesson for the week, the teacher revises the entire lesson and links it to the following week’s lesson.

 

 

NEXT LESSON

 

 

LESSON EVALUATION 

As stated the lessons.