Data presentation (Revision) Range of a set of values

Subject:

MATHEMATICS

Term:

First Term

Week:

Week 8

Class:

JSS 3 / BASIC 9

Previous lesson: Pupils have previous knowledge of

TRIGONOMETRY

that was taught in their previous lesson

Topic:

Behavioural Objectives:

At the end of the lesson, learners will be able to

• Explain Data presentation (Revision)
• Explain Range of a set of values
• Solve simple mathematics questions on the given topic

Instructional Materials:

• Wall charts
• Pictures
• Related Online Video
• Flash Cards

Methods of Teaching:

• Class Discussion
• Group Discussion
• Asking Questions
• Explanation
• Role Modelling
• Role Delegation

Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum
• Workbooks

CONTENT:

WEEK 8

TOPIC: Statistics

CONTENT:

• Data presentation (Revision)
• Range of a set of values

DATA PRESENTATION

RANK-ORDERED LIST

Rank order means arranging data values from the highest to the lowest.

A rank-ordered list is a list in which the items are sorted according to their importance or relevance. The most important item is typically listed first, followed by the second most important item, and so on. Rank-ordered lists can be used for many different purposes, including to prioritize tasks, make decisions, and organize information.

Example

Some JCSE students scored these grades in a revision test: C, B, D, A, C, C, E, B, D, F, B, D, E, C, A, C, D, B. Represent the data in rank order.

Solution

Here is the rank order list from A to F:

A, A, B, B, B, B, C, C, C, C, C, D, D, D, D, E, E, F

FREQUENCY TABLE

A frequency table is a chart that shows how often something occurs. It can be used to show data from an experiment, survey, or other data collection. Frequency tables can be used to help organize and understand data.

Frequency tables can be used to find patterns in data. For example, if you are looking at the results of a survey, you might use a frequency table to see how many people answered each question. You can also use a frequency table to compare two sets of data.

A frequency table shows the number of times a value appears. A frequency table can be prepared for a give data set data either vertically or horizontally.

Example

In a class of 30 students seated in six rows of five students each, the class monitor records the following dates of births, row by row.

Wed.          Thur.             Sun.           Tue          Fri.

Mon.          Wed.             Tues.         Fri.           Sun.

Sun.            Wed.             Mon          Tues.       Sat.

Fri.              Sat.                Sun.           Thur.      Wed.

Mon.          Sat.                Sun.           Fri.          Mon

Represent the above data in a frequency table.

• How many students were born on Tuesdays?
• In what date were most students born?
• In what date were the least number of students born?

Solution:

GRAPHS:

Graphs are a visual way of representing data and can be used to represent mathematical relationships in a simple and effective way. By plotting points on a graph, we can see the relationship between two variables and understand how they change in relation to each other. Graphs can be used to teach many different concepts in mathematics, such as linear equations, quadratic equations, and polynomials.

There are many different types of graphs that can be used to represent data, such as line graphs, bar graphs, and scatter plots.

A graph is a pictorial representation of statistical data clearly. Graphs are often more helpful than list or tables. For this stage, Graphs include:

1. Pictogram
2. Bar Chart
3. Pie chart

PICTOGRAM

In a pictogram, pictures represent the frequency of data values

Example:

Study the frequency below and represent the information in a Pictogram

A

B

C

D

E

F

BAR CHART

In a bar chart, the height (or length) of a bar represents the frequency of the data values.

Examples:

Study the frequency below and represent the information in a Pictogram

PIE CHART

In a pie chart, a circle represents all the data, and the sizes of its sectors are proportional to each item.

 Example:

1. The table below shows the number of fruits sold in a day by a fruit seller.

Illustrate the information on a pie chart.

Solution:

Total number of fruits

We need to convert the fruits’ numbers to degrees ie the sectorial angles

For Apples:  ⁰

For Bananas:  ⁰

For Mangoes: ⁰

For Oranges: ⁰

For Pawpaws:  ⁰

For Pineapples:  ⁰

HISTOGRAM.

A histogram is a tool for data representation usually made up of rectangular bars of different height conveying the proportion of the frequencies of items being represented without spaces in between bars.

Example:

The below table shows the number of students admitted in a University according to departments.

Illustrate the information on a histogram.

Solution:

CLASS ACTIVITY

1. From the list of scores given below, create a (i) rank ordered list (ii) frequency table

29, 75, 36, 70, 37, 66, 39, 64, 47, 63, 47, 47, 58, 52, 54

2. Represent the information below in (i) pictogram (ii) bar chart (iii) Pie chart (iii) Histogram

RANGE OF A SET OF VALUES

Range — The range of any set of data is the difference between the largest value and smallest value. For instance, given the set of numbers:

5, 8, 3, 2, 17, 9, 13, 6, 4

Range = 17 – 2 = 15

Sometimes the range is written as 2 → 17, meaning that the data ranges from 2 to 17.

Class Activity:

1. The raw scores of 20 pupils in a Mathematics test are:

6, 8, 10, 5, 2, 10, 6, 9, 4, 3, 10, 5, 6, 9, 8, 7, 7, 6, 6, 3

(a)  Arrange the scores in the order of magnitude starting with the smallest.

(b)  Arrange the scores in the order of magnitude starting with the largest.

(c)  What is the difference between the least and the highest scores?

(d)  How many pupils scored less than 6?

(e)  How many pupils have the lowest score; and how many have the highest score?

(f)  If the pass mark is 7 how many failed and how many passed?

2. The raw scores of 20 pupils in a Basic Science test are:

16, 8, 10, 5, 4, 20, 16, 9, 14, 13, 10, 5, 6, 19, 28, 12, 17, 22, 11, 13

(a)  Arrange the scores in the order of magnitude starting with the smallest.

(b)  Arrange the scores in the order of magnitude starting with the largest.

(c)  What is the difference between the least and the highest scores?

(d)  How many pupils scored less than 20?

(e)  How many pupils have the lowest score; and how many have the highest score?

(f)  If the pass mark is 15 how many failed and how many passed?

Assignment

1. The following records represent the number of different motor cycles (Okada) purchased in a year from one dealer:

1. How many motor cycles were purchased?
2. Illustrate the information on (i) pictogram (ii) bar chart (iii) Pie chart (iii) Histogram
3. What is the range of the number of motorcycle purchased?
4. The table below shows a survey of the favorite subjects of students in basic 2.

1. Illustrate the information on (i) pictogram (ii) bar chart (iii) Pie chart (iii) Histogram
2. What is the range of the number of motorcycle purchased?
3. In a class of 30 students seated in six rows of five students each, the class monitor records the following dates of births, row by row.

Wed.          Thur.             Sun.           Tue          Fri.

Mon.          Wed.             Tues.         Fri.           Sun.

Sun.            Wed.             Mon          Tues.       Sat.

Fri.              Sat.                Sun.           Thur.      Wed.

Mon.          Sat.                Sun.           Fri.          Mon

           Dates of birth of 30 Students

1. How many students were born on Tuesdays?
2. In what date were most students born?
3. In what date were the least number of students born?
4. What is the range of the dates of birth?
5. Draw a frequency table to represent the data.
6. Using the frequency table, Illustrate the information on (i) pictogram (ii) bar chart (iii) Pie chart (iii) Histogram.

WEEK 9

PRESENTATION:

Step 1:

The subject teacher revises the previous topic

Step 2:

He or she introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

CONCLUSION:

The subject goes round to mark the pupil’s notes. He does the necessary corrections