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Alle Oberthemen / Mathematics / Handling Data

AQA Module 1 (Higher) (14 Karten)

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How do you draw a cumulative frequency graph? (Part 1)
Given this set of data...

Time, t Frequency Cumulative Frequency
0< t ≤10 22 22
10< t ≤1532 54
15< t ≤2026 80
20< t ≤251595
25< t ≤305100


For cumulative frequency graphs, remember to plot your points at the TOP of each class boundary, DO NOT use midpoints.

See Part 2 of this card for the actual graph
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How do you draw a cumulative frequency graph? (Part 2)
Here is the actual graph

Notice it starts with a cumulative frequency of zero from the top class boundary of the class below.
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Why are moving averages useful?
They show a general trend and/or remove seasonal variations.
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What is a frequency diagram?
If you are asked to draw simply a frequency diagram, then you may draw either a frequency polygon or a frequency histogram (equal-width bars with no gaps).

You must read the question very carefully. Make sure you're doing the right type of graph.
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How do I calculate the estimated mean of grouped data?
Given this set of data for the test marks of a class of students, find an estimate for the mean test score of the class.

Mark (m)Number of studentsMidpointFreq x midpoint
0<m≤25412.54x12.5=50
25<m≤355305x30=150
35<m≤40837.58x37.5=300
40<m≤45542.55x42.5=212.5
45<m≤60152.51x52.5=52.5
Totals:23 765

To actually calculate the mean...
Total of (frequency * midpoint) column ÷ Total Frequency
765 ÷ 23 = 33.3 (1 d.p.)


Always check your answer makes sense
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How do I calculate mean from a frequency table?
A school recorded the number of days that Year 9 pupils were absent last week.
Calculate the mean number of days absent


Number of days Number of pupils No of days x No of pupils
0 144 0x144=0
1 27 1x27=27
2 18 2x18=36
3 8 3x8=24
4 2 4x2=8
5 1 5x1=5
Total:200 100

To find the mean...
Sum of (number of days x number of pupils) ÷ Number of pupils
100÷200=0.5


Notice that no midpoints are needed as this is not grouped data.
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For what type of data are histograms suitable?
Histograms can only be used for continuous data.

Frequency density histograms are useful where class widths are not equal.
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How can probabilities be given?
Probabilities can be given as:

* Fractions
* Decimals
* Percentages


NEVER give a probability as anything else (including ratio).
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Key features of different graph types
Histograms:
No gaps between bars.

Frequency Histograms:
Equal bar widths.
Frequency as y-axis

Frequency Density Histograms:
Different bar widths.
Frequency Density as y-axis

Cumulative Frequency graphs:
Points plotted at top of class-boundaries.
Smooth curve through points.

Frequency Polygons:
Frequencies plotted at class mid-points.
Points joined with straight-lines.
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Why is a 7-point moving average appropriate for the daily sales of a shop?
If you get a question, for example, asking why a 7-point moving average is appropriate, it's probably something to do with there being seven days in a week.

A 4-point moving average is often used for seasons (Autumn, Winter, Spring, Summer) because there  are 4 of them.

Make sure you're answering the question though.
Why do we use a moving average?
is a different question to
Why is a 4-point moving average appropriate to this data?

For the second question, you must be specific as to why a four point moving average is used.
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How do I calculate a 4-point moving average?
Answer
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How can I use a moving average to find an original value?
Answer
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How do I complete a tree diagram?
Answer
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How do I use a tree diagram to calculate probabilities?
Answer
Kartensatzinfo:
Autor: mrfoxton
Oberthema: Mathematics
Thema: Handling Data
Veröffentlicht: 18.10.2009
Tags: AQA GCSE Module 1 Higher Revision
 
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