16 Cumulative Frequency Worksheet Page 7
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27MEP Y9 Practice Book B
16.2
The frequency polygon is shown below. We obtain it by joining the midpoints of
the tops of the bars from the previous graph.
Frequency
12
11
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Time (hours)
Example 2
At a school fair, visitors enter a 'Guess the weight of the cake' competition. Their
guesses, rounded to the nearest 100 grams, were recorded in the following table:
Guess (kg)
0.5 - 0.7
0.8 - 1.0
1.1 - 1.3
1.4 - 1.6
1.7 - 1.9
Frequency
5
32
26
11
6
(a)
Illustrate the data using a bar chart.
(b)
Estimate the mean of the data.
(c)
State the modal class.
Solution
(a)
The guesses have been recorded to one decimal place, in other words to the
nearest 100 grams. This means that the first category, nominally described
as '0.5 - 0.7 kg' actually includes guesses greater than or equal to 0.45 kg but
less than 0.75 kg. The precise description of the first category is therefore
≤
<
0 45
.
kg
guess
0 75
.
kg
The nominal descriptions of the other classes must also be interpreted
precisely if we are to represent the data accurately.
≤ <
≤ <
≤ <
≤ <
≤ <
Guess (kg)
0 45
.
G
0 75
.
0 75
.
G
1 05
.
1 05
.
G
1 35
.
1 35
.
G
1 65
.
1 65
.
G
1 95
.
Frequency
5
32
26
11
6
The precise descriptions of the classes indicate how the bars should be
drawn on the bar chart.
174
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