Sample Lesson Plan

Title

Monthly Salary

Level

Key Stage 3

Domain

Frequency Polygon, Frequency Curve, Histogram, Mean, Mode (Modal Class), Median (for grouped data)

Objectives

  1. To use histogram, frequency polygon and/or frequency curve to present the distribution of a set of data.
  2. To discuss the central tendency of a set of data.
  3. To use the measures of central tendency to investigate the “average” or ”typical” salary in a certain population.

Prerequisite Knowledge

Frequency Table (for grouped data)

Data Source

Datasets from Census and Statistics Department, HKSAR.

Dataset 1: Monthly income (from main employment) by industry and sex in year(?)

Dataset 2: Monthly income (from main employment) by educational attainment and sex in year(?)

Dataset 3: Monthly income (from main employment) by occupation and sex in year(?)

Dataset 4: Monthly income (from main employment) by age and sex in year(?)

Dataset 5: Monthly household income by district in year(?)

Dataset 6: Monthly household income by household size in year(?)

[Data are grouped instead of raw figures. While we are still seeking approval of direct access to the “original” (yet aggregated or grouped) data from the Census and Statistics Department, the size and structure of these datasets can be understood from Tables C15–C19, D2 and D4 in 1996 Population By-census: Main Tables. There is a problem yet to be solved (with assistance from the CSD): unequal intervals (or classes) in dividing the income/salary scale.]

Preparation

Visit the website of Census and Statistics Department, HKSAR, to gather some background information about statistical survey done by the department in Hong Kong. In particular, you will find the sections “Labour and Employment” and “Wages” under Frequently Asked Statistics (and also in Chinese) useful and relevant to the present investigation into Monthly Salary. Latest press release on the topic can also be found on the site.

Try to gain gather information concerning the following questions:

How often are statistical surveys on the issues concerned conducted by the Census and Statistics Department?

How are such surveys conducted?

In what ways are the data on wages and salaries organized?

What is the use of the results of such surveys?

You may wish to have a look into the datasets so that you can gain a basic understanding of how “monthly income” is considered in association with different age groups, different levels of educational attainment, different industries and occupations. Precisely speaking, you need to know what kind of industries and occupations can be found in the pre-determined categories of the CSD data.

Motivation

(a)We have billionaires as well as the extreme poor in the city. Ask the students to have a guess of the salaries of some government officials and some people they are familiar with, e.g. school teachers. (All these can be referred to the master-pay scale.) But how about the others – the average people?

(b)By raising a few typical examples of job positions in Hong Kong, ask the students to have a guess of the monthly income in each case.

(c)Ask the students to guess the average monthly income of each of the following:

–a school leaver completed his/her lower-secondary studies (say S3)

–a school leaver graduated at upper-secondary level (say S5)

–a school leaver graduated from the sixth form

–a university graduate

Main Tasks

Task 1

  1. Ask the students to work in 8 groups (each of 4–6). Each group is asked to work on the data on monthly income (from main employment) for one industry (from Dataset 1) and give a graphical presentation of the data for that particular industry. Ask the students to consider carefully the following questions:

How do they go about the sex-differentiated data given in the dataset? Do they consider the difference significant?

What kind of graphs/charts will they consider useful? Why?

  1. After presentations done by each group, discuss with the students the strengths and weaknesses of the graphs/charts they used. Also, by taking a few examples of their graphical displays, discuss with them the meaning of “central tendency”.
  2. With their graphical displays, ask each group to make an estimate for the average monthly income of people in that particular industry. Then, ask the students to work out the summary statistics, namely, the mean, the modal class, and the median, for the monthly income of people in the industry, using the toolkit provided by Stat.Net. Discuss with the students the differences among the three measures of central tendency, together with their different meanings relevant to the social context. Do these figures agree with their commonsense understanding of our society?
  3. Work out the measures of central tendency for the “total”, i.e. by pooling all the people in different industries together. Also compare these measures with those found in (3).

Task 2

Given Dataset 2 , the students are going to do the same kind of investigation but focussing at different levels of educational attainment. Each of the eight groups of students is asked to work on either of the seven pre-determined levels of educational attainment or the set of values for the total. Discuss with the students any findings out of the distribution and measures of central tendency of monthly income at different levels of educational attainment.

Task 3 (Optional)

Take a particular dataset and investigate the effects on the measures of central tendency if there is an overall increase of salaries across the whole group by

(a)a certain amount, e.g. $1000;

(b)a certain percentage, e.g. 8%.

Exercise

  1. Choose three occupations listed in Dataset 3. (You may like to choose three with which you are more familiar.) For each of the three occupations you choose,

(a)give your estimate of the average monthly income of a person in that occupation,

(b)detemine whether you will take the sex difference into consideration and give your reasons,

(c)work out the three different measures of central tendency of monthly income in that occupation, and discuss your findings.

  1. From Dataset 4, choose three age groups which you think will result in rather different monthly income. By working out appropriate measure(s) of central tendency of monthly income, discuss the differences you have noticed among the three age groups.
  1. Dataset 5 gives data of monthly household income in different districts. Which district do you think is the “richest”? By using appropriate measure(s) of central tendency of monthly household income, compare it with some other districts.
  1. Dataset 6 gives data of monthly household income for different household size. Do you think the average monthly household income inreases steadily with the household size?

Enrichment

Investigate the changes of average monthly income of people in Hong Kong over the last twenty years. The investigation can be based on data of monthly income for some chosen groups of people (be it a particular age group, a group at certain level of educational attainment, a particular occupation, or whatever) in a few separate years. [It depends on what sort of data will be further provided by the Census and Statistics Department.]

Further comparison across different cities (e.g. Singapore) can also be carried out. (Data in other countries can be found on the Internet.)

Proposed Follow-up Project

An anonymous survey can be conducted within the class or within the form. Each student tries to get the monthly salary of at least one member of his/her family, together with some of his/her particulars, e.g. age, sex, occupation and/or educational level. Having the information entered in the on-line survey, students are required to analyse the data collected and prepare presentations and reports on their findings.

Remarks

  1. The difference between the measures of central tendency depends on the dispersion and the skewedness of the distribution. The effect of outliers is one of the significant factors and thus needs to be taken into consideration in the discussion. In this connection, teachers must have an idea of the extent to which outliers affect the distributions in different situations.
  2. Apart from histograms, frequency polygons or curves may also be constructed for the graphical presentation of the grouped data.

Lesson Plan (KS3): Monthly Salary– 1 –2nd Draft