Year 9 Mathematics Booster level 4  5
Handling Data
OBJECTIVES




Find the mode, median and range (level 5)
Calculate the mean (level 5)
Interpret tables, graphs and diagrams for both discrete and continuous data, and
draw inferences that relate to the problem being discussed; relate summarised data
to the question being explored (level 5)
Compare two distributions using the range and one or more of the mode, median
and mean (level 5)
VOCABULARY

Mode, median, mean, range, compare, greater, less, slightly, significantly
RESOURCES

Whiteboards, OHT
ORAL AND MENTAL STARTER
10 mins
1. First ask pupils to explain what is meant by the mode, median, range, mean.
2. Next, list a set of numbers on an OHT or board, for example: 5, 9, 10, 7, 9.
Q
What is the mode (median, range, mean) of this set of numbers?
You may want pupils to display answers on whiteboards.
Repeat for 15, 19, 21, 17, 19.
Q
How did you work out these answers?
Repeat for a different set of numbers.
MAIN TEACHING
40 mins
Q
Sam has six cards, each of which has a positive whole number printed on it.
Four of the cards have the number 10. Without knowing the numbers on the
other two cards can you give the value of the median, mode and range?
Explain your reasoning.
Q
The six cards have a mean of 10. What can the numbers on the other two
cards be? Discuss possible answers. Which answer would give the greatest
range? Why?
1. Introduce the chart on OHT M14.1 of the lengths of 100 words in two
newspapers.
2. Ask pupils, in pairs, to describe what the chart shows.
3. Allow a few minutes for them to consider and discuss their answers.
4. Note how pupils’ comments may clarify the context of the chart.
5. Organise their statements into factual points extracted from the chart and
those points that involve a comparison.
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Q
Handling Data
What does comparing mean?
1. Collect ideas and ensure that ideas of what is similar and what is different are
included.
2. Explain that when quantities differ they may be greater or less and the
difference may be slight or significant.
Look back at some of the statements and develop them so that they are more explicit.
For example:

Broadsheet newspapers have more occurrences of significantly longer words,
i.e. of 7 and 8 letters, than tabloid newspapers.

Broadsheet and tabloid newspapers have similar numbers of shorter words,
i.e. of 1 or 2 letters.

The modal length of word for both types of newspaper is 3.
Explain that it is important to draw inferences from the data.
Q
Q
Why do tabloid newspapers choose to use shorter words?
Why do you think the modal length of word is 3 for both types of newspaper?
NB Pages 261 – 270 of the Framework supplement provide further examples on interpreting
graphs, as do Key Stage 3 test questions.
Worksheet J2
PLENARY
10 mins
1. Show OHT M14.2 ‘Method of travel from the UK’.
You may choose to use the question as set or by removing some of the
structure you can develop pupils’ skills in using and applying mathematics.
2. Show OHT J1 ‘Two Towns’
Use the question as set to compare distributions using the range, median and
mean.
Buckinghamshire Secondary Mathematics Curriculum Resources
Year 9 Mathematics Booster level 4  5
Handling Data
Handling Data Worksheet J2
1.
Nasser plays cricket and in his last four innings he has made the following scores:
35
32
7
50
a) Calculate his mean score
b) Calculate his median score
c) Nasser’s mean must be at least 40 to stay in the England team and he has
one more innings left. Calculate how many runs he needs to score if he is
to keep his place in the side.
2.
Copy and complete the following sets of data so that the statistics shown are correct.
(Each question mark represents one missing number)
a)
b)
c)
d)
e)
3.
3, 4, 5, 6, ?
3, 5, 2, 8, 1, 2, ?
30, 28, 32, 29, ?, ?
87, 87, 88, 88, 89, ?
4, 5, 6, 7, ?, ?
with
with
with
with
with
Range = 7, Median = 5
Mean = 4
Mode = 28, Mean = 30
Range = 2, Mode = 88
Mean = 4.5, Mode = 4
Here is a bar chart showing rainfall
Rainfall
Kim draws a dotted line on
the bar chart. She says: “The
dotted line on the chart shows
the mean rainfall for the four
months.”
mm of rain
25
20
15
Use the chart to explain why
Kim cannot be correct.
10
5
0
May
June
July
August
Month
4.
A newspaper does a survey to find out the ages of its readers. This is the chart they
print.
100%
80%
50 and over
60%
40 to 49
40%
30 to 39
20%
under 30
0%
Men
Woman
(a) The chart shows that 12% of male readers
are aged 30 to 39. Roughly what percentage
of female readers are aged 30 to 39?
(b) The newspaper asked an equal number of
males and females. Why would they do this?
(c) There are 50,000 male readers aged 50 or
over. Estimate the number of male readers
aged 40 to 49.
(d) Chris says: “Male readers are generally
younger than female readers.” Is he right?
Give a reason for your answer.
Buckinghamshire Secondary Mathematics Curriculum Resources