Lesson Notes By Weeks and Term - Senior Secondary 1

Data collection and presentation

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Term: 1st Term

Week: 7

Class: Senior Secondary School 1

Age: 15 years

Duration: 40 minutes of 2 periods each

Date:       

Subject:      Economics

Topic:-       Data collection and presentation

SPECIFIC OBJECTIVES: At the end of the lesson, pupils should be able to

  1. Define the various measures of central tendency
  2. Perform calculations involving the various measures of central tendency

INSTRUCTIONAL TECHNIQUES: Identification, explanation, questions and answers, demonstration, videos from source

INSTRUCTIONAL MATERIALS: Videos, loud speaker, textbook, pictures

INSTRUCTIONAL PROCEDURES

PERIOD 1-2

PRESENTATION

TEACHER’S ACTIVITY

STUDENT’S ACTIVITY

STEP 1

INTRODUCTION

The teacher reviews the previous lesson on the basic tools for economic analysis

Students pay attention

STEP 2

EXPLANATION

She defines the various measures of central tendency

 

Students pay attention and participates

STEP 3

DEMONSTRATION

She performs calculations on each

Students pay attention and participate

STEP 4

NOTE TAKING

The teacher writes a summarized note on the board

The students copy the note in their books

 

NOTE

MEASURES OF CENTRAL TENDENCY

Measures of central tendency means are values which show the degree to

which a given data or any given set of values will converge toward the

central point of the data. It is also called measure of location and is the

statistical information that gives the middle or centre or average of a set of

data. It includes mean, median and mode.

 

THE MEAN

Mean or arithmetic mean is defined as the sum of series of figures divided

by the number of observations. It is the commonest and the most widely

used among the other types of averages or measures of central tendency.

 

TYPES OF MEAN

  1. The Arithmetic Mean
  2. The Geometric Mean
  3. The Quadratic Mean

 

Example

Calculate the arithmetic mean of the following scores of eight students in

an economics test. The scores are: 14, 18, 24, 16, 30, 12, 20, and 10.

 

Solution

Add up the scores

14+18+24+16+30+12+20+10 = 144

Number of observation (students) = 8

Arithmetic Mean =Sum of observations divided by Number of observations

=   144/8   =18

 

ADVANTAGES OF THE MEAN

  1. It is easy to derive or calculate.
  2. It is easy to interpret.
  3. It is the best-known average.
  4. It has determinate exact value.
  5. It provides a good measure of comparison.

 

DISADVANTAGES OF THE MEAN

  1. It is difficult to determine without calculation.
  2. Some facts may be concealed.
  3. It cannot be obtained graphically.
  4. If one or more value is incorrect or missing, the calculation becomes difficult.
  5. It may lead to distorted results.

 

THE MEDIAN

The median is an average which is the middle value when figures are

arranged in their order of magnitude either in ascending or descending

order, especially from ungrouped data.

 

ADVANTAGES OF THE MEDIAN

  1. It is easy to determine with little or no calculations
  2. It is easy to understand and compute
  3. It does not use all values in the distribution
  4. It gives a clean idea of the distribution

 

DISADVANTAGES OF THE MEDIAN

  1. It is not useful in further statistical calculation
  2. It ignores very large or small values
  3. It does not represent a true average of the set of data.

 

THE MODE

This is the most frequently recurring number in a set of numbers or data,

that is to say, it is the number or value with the highest frequency. It tells us

the observation which is most popular. The best and easiest way of

calculating the mode of any distribution is to form a frequency table for it.

 

ADVANTAGES OF MODE

  1. It can be easily understood.
  2. It is not affected by extreme values.
  3. Easy to calculate from the graph.
  4. It is easy to determine.

 

DISADVANTAGES OF MODE

  1. It can be a poor average.
  2. It can be difficult to compute if more than one mode exists.
  3. It is not useful in further statistical calculations.
  4. All the values used in the distribution are not considered.

 

FORMULATION OF FREQUENCY TABLE FOR UNGROUPED DATA

UNGROUPED DATA: 

Ungrouped data is one in which the raw data has occurrences or

frequencies more than and are without class intervals. In the formulation of

a frequency table for ungrouped data, two basic steps are taken.

  1. Prepare a tally sheet.
  2. Prepare a frequency table.

 

PREPARATION OF A TALLY SHEET: This is when the variables are taken one after the other with a stroke called tally. The tally of five makes a bundle.

 

PREPARATION OF A FREQUENCY TABLE: The frequency table is simply obtained by adding the tallies together in a separate column referred to as frequency.

 

Example: The following are scores of thirty (30) students of SS 1 in an

economics test.

2, 4, 8, 8, 2, 6, 6, 8, 2, 4

8, 0, 8, 6, 0, 10, 2, 2, 0, 10

4, 6, 0, 10, 2, 2, 6, 6, 4, 2

  1. Prepare a frequency table inclusive of a tally
  2. Find the mean
  3. Find the mode
  4. Find the median

 

SOLUTION

NUMBERS

FREQUENCY

TALLY

0

4

////

2

8

//// ///

4

4

////

6

6

//// /

8

5

////

10

3

///

 

  1. Arithmetic mean = 0 x 4 + 2 x 8 + 4 x 4 + 6 x 6 + 8 x 5 + 10 x 3

                                                          30

                             = 0 + 16 + 16 + 36 + 40 + 30

                                                 30

                             = 138

                                 30

                             = 4.6

 

  1. Median = 4 + 4

                      2   

                = 8

                   2

                = 4

  1. Mode = 2

EVALUATION:    1. Define the following measures of central tendency

                       a. Mean

                       b. Median

                       c. Mode

  1. Discuss two advantages and disadvantages each of

       a. Mean

       b. Median

       c. Mode

       3. The following are scores of 20 students in an Economics test.

                           5          10        2          9          5          3          4         

                           6          1          3          2          3          6          1         

                           3          3          2          3          4          3

         a. Prepare a frequency table with tally

                             Find the

         b. Mean

         c. Median

         d. Mode

 

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively