The Mode

1
The Mode

• The mode is a type of average
• The mode is the value that occurs most often in
  a set of data
• Example

5, 6, 8, 2, 4, 5, 3, 5
MODE 5
Sometimes there is no mode because all the values
are different There can be more than one mode
2
Modal Class
For grouped data such as the example below, we
cannot find the mode.
Modal class 3-5
Instead, we find the MODAL CLASS. This is the
group that occurs most often.
3
The Mean

• The mean uses all the items of data.
• Mean Total of all items of data
• The number of items of data
• 2,4,4,8,7,2
• Mean 27 6
• 4.5

4
Finding the Mean
Remember, when finding the mean of a set of data,
we add together all the pieces of data.
This tells us that there were nine 1s in our
list. So we would do 111111111 9
It is simpler to use 1x9!!
We can do this for every row.
5
Finding the Mean
107
40
6
Calculating the Mean

• Mean Total of frequency X Number of tests
• Total Frequency

The Mean is
107 40 2.7 (1dp)
7
The Median

• The median is another type of average
• The median is the middle value for a set of data
  when the values are put in numerical order.

Example
6, 8, 3, 7, 5, 2, 4 in order
2, 3, 4, 5, 6, 7, 8
Median 5
For an odd number of values in data set, there is
only one middle value. This is the median.
8
What is the median test score for the following
set of results?
5, 7, 7, 8, 10, 12, 14, 15
Median 9
For an even number of values in a data set, there
are two middle values.
The median is the value in the middle of these
two values.
9
The Range

• The range is not an average.
• The range of a set of data is the largest value
  minus the smallest value.
• It shows how the data is spread out.

A small range shows
that the values in a set of data are similar in
size
A large range shows
that the values differ considerably
10
Estimated mean

• grouped data so the mean is estimated.

Total 50 2945
Estimated mean sum of mid-point x freq
total frequencies

2945 58.9seconds 50
11
Example - drawing a stem and leaf
Completion times
3 4 5 6 7
8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
7 3 7 4 8 1 2 1 8 3 5 2
Dont forget the key
Completion times
47 means 47
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
12
Example - drawing a stem and leaf
47 means 47
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
The median is the middle value
There are 29 values
i.e. 15th value
Median
47
13
Example - drawing a stem and leaf
Range Highest - Lowest
47 means 47
Completion times
3 4 5 6 7
8 1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
9 1 2 3 4 7 8 1 3 5 8 2
Range 72 38 34
14
Rather than using words we use numbers on the
probability scale
Impossible Certain
0 0.5 1
The probability of an event occurring is written
as a fraction, a decimal or a percentage,
e.g.The probability of getting an even number
on rolling a dice is ½ or 0.5 or 50
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How likely?

• Number of ways it happensNumber of things
  that can happen

The probability of getting an even number when a
dice is rolled P(even number) 3 6 (or ½ or
50 or 0.5) The probability of selecting a
diamond from a standard pack of cards P(diamond)
13 52 (or ¼ or 25 or 0.25)
16
Remember the total of all the probabilities is 1

• The team must win, lose or draw.
• P(Win) P(Lose) P(Draw) 1
• 0.3 0.5 P(Draw) 1

This is 0.5
This is 0.3
So this must be 0.2
17

•  If a dice is rolled 300 times, how many times
  would you expect to roll a number greater than
  4?P (numbergt 4) 2/6 1/3
• Expected no. of successes
• p (success) number of trialsExpected number
  of scores greater than 4 1/3 300 100 

18
Makes of car in a school car park
Construct a pie chart to show this information. A
full circle is 360o There are a total of 3241
10 cars 360 10 36 We use 36o to represent
each car
360o
19
Makes of car in a school car park
3x36o108o
2x36o72o
4x36o144o
1x36o36o
We use 36o to represent each car so the3
Cavaliers are represented by 3x36o 108o Work
out the angle needed for each of the other models
of car
20
Makes of car in a school car park
Mark the centre of the pie and draw the
circle. Draw a line from the centre to the
edge Measure the first angle needed (108o) Draw
in the line and label the section
Cavalier
108o
21
Makes of car in a school car park
From this line measure the next angle, draw the
line and label the section. Continue in this
way Check that the last section has the correct
angle and label it.
Volvo
36o
Cavalier
Rover
144o
72o
Ford
22
Interpreting Pie Charts

• 20 pupils in class 3B travel to school. From the
  chart find the number of pupils who travel by
  each method.
• Walk
• Cycle
• Bus

23
Scatter Graphs

• Positive correlation
• We have seen that as the temperature increases,
  the number of ice-creams sold increases. The
  results are approximately in a straight line,
  with a positive gradient. We therefore say that
  there is positive correlation.

24
Negative correlation

• There is a definite a connection between the two
  sets of data, as the results are approximately in
  a straight line. As the number of weeks
  increases, sales decrease. The line therefore has
  a negative gradient, and we say there is negative
  correlation.  

25
No correlation

• It is obvious that there is no connection between
  these values, and this is shown by the scatter
  diagram. We say there is no correlation.  

26
Lines of best fit

• The 'line of best fit' is a line that goes
  roughly through the middle of all the scatter
  points on a graph. The closer the points are to
  the line of best fit the stronger we can say the
  correlation is.
• DO NOT JOIN THE POINTS UP!

27
Sampling

• Random
• Use the RAN button X the population size.
• Round the number and repeat for the sample size
  required.
• Systematic-
• Population size Sample Size
• Tells you the gap to leave between the items of
  data you collect for your sample.

28
Exam Technique

• Show all your workings on the paper.
• Write in blue or black ink, use pencil for graphs
  and charts
• Look at the number of marks for each question and
  write the appropriate number of points
• Check that your answers are sensible. (Especially
  for averages questions, make sure your answer is
  in the range available)
• Show your method clearly especially on the
  calculator paper (you get marks for the correct
  method even if the answer is wrong)
• Dont panic. If you cant do a question leave it
  until later.
• Good Luck!