Key Stage 3
Data Handling Dimension
Learning Unit: Measures of Central Tendency
Learning Objectives:
• find mean, median and mode from a given set of ungrouped
data
•
find mean, median and modal class from a given set of
grouped data
• be aware that the mean found for grouped data is an estimation
•
discuss the relative merits of different measures of central
tendency for a given situation
•
explore and make conjectures on the effect of the central
tendency of the data such as
(i) adding a common constant to the whole set of data;
(ii) multiplying the whole set of data by a common constant;
Programme Title: Measures of Central Tendency
Programme Objectives
1. Use daily life examples to recognize the meaning of and to find the mean,
median and mode from a given set of ungrouped data.
2. Use daily life examples to find the mean, median and mode from a given set
of grouped data.
3. Use daily life examples to explain that the mean found for grouped data is
only an estimation.
4. Discuss the relative merits of different measures of central tendency for a
given situation
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5. Explore the effect of the central tendency of the data when
(i)
adding a common constant to the whole set of data;
(ii)
multiplying the whole set of data by a common constant;
Programme Content
The programme uses a story of the training of a basketball team to introduce the
measures of central tendency. In appointing a team captain, they consider the
averages of the heights of the team members. The heights are used as a set of
ungrouped data for calculating the averages which include the mean, the
median and the mode. These three averages are the measures of the central
tendency of their heights.
The programme uses various daily-life experiences such as the mean cost of a
meal, the median of salaries and the mode of shoe sizes to illustrate the
calculation of mean, median and mode. It focuses on the understanding and
interpretation of statistical information. Pupils are led to explore the effect of
the central tendency of a set of the data when adding a common constant to the
whole set of data; or multiplying the whole set of data by a common constant.
The programme brings forth a common example of a set of grouped data
collected from an ordinary survey. As an extension of the content of another
ETV programme on “Statistical Diagrams & Graphs”, this programme further
introduces the constructions of frequency distribution table, cumulative
frequency distribution table and cumulative frequency curve. The calculation of
mean, median and mode of a set of grouped data is then elaborated. Finally, the
programme encourages the enquiry on the characteristics, appropriateness and
effectiveness of the uses of different averages in different situations.
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Worksheet Answers
(1)
(a)
(b)
(c)
mean = 5.5, median = 5.5, modes = 2 and 9;
mean = 15.5, median = 15.5, modes =12 and 19;
mean = 27, median = 27, modes = 10 and 45.
(2) (a) mean; (b) mode
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Key Stage 3 ETV Programme
《Measures of Central Tendency》
Worksheet
1. Find the mean, median and mode of the following set of data.
1，2，2，4，5，6，7，9，9，10
(a)
mean = ________, median = ________, mode = _________
(b) If 10 is added to each datum, then
mean = ________, median = ________, mode = ________
(c) If each datum is multiplied by 5, then
mean = ________, median = ________, mode = ________
What are the effects on the averages of a set of data when a constant is
added to each datum or when each datum is multiplied by a constant?
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2.
Salaries of the employees in a basketball club
Salary($)
7500
8000
14000
30000
No. of employees
4
15
3
3
The above table gives the information of the salaries of the employees in a
basketball club.
(a) The club chairman calculates that the employees’ average income is $11280.
Which type of average does he use?
(b) The staff representative calculates that their average income is only $8000.
Which type of average does he use?
(c)
Which type of average would most reasonably reflect the central
tendency of the employees’ income and which type of average would
most suitable to be use as a reference to calculate the salary adjustment?
Why?
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