NAME: ______
TUTOR GROUP: ______
Finding averages from frequency tables
There are two types of frequency tables you could get.
- Normal frequency tables
e.g. the number of goals scored in 40 matches:
The mode is the most popular number of goals so :
The median is the middle value (between the 20th and 21st), so:
- Grouped frequency tables
e.g.
The mode is the most popular age group :
The median is the middle value (between the 25th and 26th), so:
Cumulative frequency.
The table shows the lengths of 160 fish caught in a river last summer.
Length (cm) / Frequency / Cumulative frequency7 L < 15 / 14 / 14
15 L < 20 / 14 / 28
20 L < 25 / 22 / 50
25 L < 30 / 62 / 112
30 L < 35 / 34 / 146
35 L < 42 / 14 / 160
Now plot the graph:
This information can now be put on a box plot:
Census and Sampling
A CENSUS is where you survey EVERY ITEM FROM THE GROUP OR POPULATION
SAMPLING is about selecting a small number items or people from a larger group for a survey.
Simple random samples.
This is where you take your sample randomly from the group.
You could do this by:
- Numbering everyone and selecting the sample using random numbers (e.g. from calculator)
- Placing all items in a hat and picking out the sample.
Stratified random samples.
This is where the group has been put in categories and the sample must be taken in a way which takes this into account.
e.g.
Time series and Moving averages.
Example
The time series and moving averages are plotted as follows:
You can use the trend line to estimate values that are not on the graph.
For example, the trend line gives a cost of £72 for December 2003
BUT, in December 2002, the actual value was £3 more that the trend line.
So the ESTIMATED COST for December 2003 = £72 + £3 = £75
Histograms
In a histogram – the AREA of the bars = frequency.
Frequency polygons
This is a diagram where the frequency is plotted on graph and joined by lines to show the ‘shape’ of the data.
Example:
Scatter diagrams and correlation
Example:
Correlation
If the points on the scatter diagram have a pattern – this is called CORRELATION:
Stem and leaf diagrams
Box plots
To draw a box plot, you need to know:
- The lowest value
- The highest value
- The median
- The lower quartile
- The upper quartile.
Example:2, 4, 8, 12, 15, 16, 18, 20, 21, 25, 27, 30, 35, 37, 40
Lower quartile medianupper quartile
This information can now be put on a box plot as follows.
Index numbers
An index number or price index is used to indicate percentage increase or decrease.
Here’s an example question:
To work out a price index use this formula: or
Here’s an example:
Probability
1) Relative frequency:
This is when probability is worked out using data from an experiment.
e.g.
2) The AND & OR rules for probability.
P(A AND B) = P(A) x P(B)For independent events
P(A OR B) = P(A) + P(B) For mutually exclusive events
e.g.
Same colour means:(Blue AND Blue)OR(Green AND Green)OR(Red AND Red)
= + +
= + +
=
3) Tree diagrams
The question above could also have been answered using a tree diagram:
First spinSecond spin