Transcript 7 - Dynamic Learning from Hodder Education

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Mean from grouped data
Continuous data
Choosing groups
Mean of continuous data
Mastering Mathematics © Hodder and Stoughton 2014
Using grouped frequency tables – Worked Examples
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For large amounts of data use a grouped frequency table.
Between 5 and 10 groups (or classes) is usually most suitable.
The modal class has the highest
frequency.
Show classes for continuous data using
“less than” < or “less than or equal to” ≤.
To estimate the mean from a grouped frequency table use the mid-interval value for
each group.
Multiply the mid-interval value by the frequency.
Add the results.
Divide that answer by the total frequency.
Round the answer for a suitable estimate.
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Mastering Mathematics © Hodder and Stoughton 2014
Using grouped frequency tables – Worked Examples
Mean from grouped data
Ronny goes to the City of London.
He records the number of floors in the buildings
near Liverpool Street Station.
Number
Tally
of floors
1–5 ///
3
1. Make a tally chart using the groups 1–5, 6–10
and so on. What is the modal class?
6–10 //// /
5
11–15 //// //
7
16–20 //// /
6
2. Calculate the mean number of floors for the
buildings.
Total
21
The modal class is 11–15 floors.
Number Mid-interval Frequency Mid-interval
of floors value
value ×
frequency
1–5
3
3
9
6–10
8
5
40
11–15
13
7
91
16–20
18
6
108
Do a similar survey of buildings in your
nearest big town or city.
Mean number of floors = 248 ÷21 = 11.8095... = 12 to the
nearest wholeTOTALS
number.
21
248
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Mastering Mathematics © Hodder and Stoughton 2014
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Using grouped frequency tables – Worked Examples
Continuous data
Are the following data discrete or continuous?
a) Foot length.
b) Shoe size.
c) The number of coins in my pocket.
d) The weight of coins in my pocket.
e) The number of heads obtained when a coin is tossed 100 times.
a) Foot length can take any value. It is continuous.
b) Shoe sizes can only take whole numbers (or
halves in British sizes). It is discrete.
c) This must be a whole number. It is discrete.
d) This could be any weight. It is continuous.
e) This must be a whole number. It is discrete.
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Mastering Mathematics © Hodder and Stoughton 2014
Answer
Using grouped frequency tables – Worked Examples
Choosing groups
Here are two sets of continuous data.
1. What intervals would you use for grouping each
set of data? Remember that between 5 and 10 is
usually suitable for the number of groups.
The range for firework times (t) is from 10 s to 35 s.
5 groups of 5 seconds is best:
10 ≤ t <15, 15 ≤ t < 20 etc.
The range for the 100 m times (t) is 13.1 s to 21 s.
5 groups of 2 seconds is best:
12 ≤ t <14, 14 ≤ t <16 etc.
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Mastering Mathematics © Hodder and Stoughton 2014
Answer
Using grouped frequency tables – Worked Examples
Mean of continuous data
The maximum temperature, in °C, is
recorded in Auckland for each day in
June and shown on the right.
1. Copy and complete this tally chart
and frequency table.
Temperature °C (T) Tally
Frequency
10 ≤ T< 12
///
3
12 ≤ T < 14
//// //
7
14 ≤ T < 16
//// //// //
16 ≤ T < 18
////
5
18 ≤ T < 20
///
3
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Mastering Mathematics © Hodder and Stoughton 2014
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Answer
Using grouped frequency tables – Worked Examples
Mean of continuous data
Below is a table ready that can be
used to work out an estimate for the
mean temperature for June.
1. What numbers should you use for
the mid-interval values?
2. Now complete
the table and
calculate your
estimate for
the mean
temperature.
11,13,15,17 and 19.
The estimate for the
mean is 422 ÷ 30
= 14.066…
= 14.1 °C to 1 d.p.
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Temperature °C
T
Mid-interval value
M
Frequency
F
M×F
10 ≤ T < 12
3
3
9
12 ≤ T < 14
13
7
91
14 ≤ T < 16
15
12
180
16 ≤ T < 18
17
5
85
18 ≤ T < 20
19
3
57
30
422
Totals
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Mastering Mathematics © Hodder and Stoughton 2014
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Using grouped frequency tables – Worked Examples
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Mastering Mathematics © Hodder and Stoughton 2014
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Using grouped frequency tables – Worked Examples