Numeracy
Application of Number
______________
L2
Workbook 15
Statistics
HD1/L2.1
HD1/L2.2
HD1/L2.3
HD1/L2.4
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
Mean, Median, Mode and Range
Mean - Add up all the numbers and divide by how many numbers there are.
Example
Find the mean of the following
6, 3, 4, 8, 2
Mean = (6 + 3 + 4 + 8 + 2) 5
= 23 5 = 4.6
Mode - The item that occurs most often
Example
1, 2, 2, 2, 3, 3, 4, 5, 6
Mode = 2 (there are more 2s than any other number)
(NB. It is possible to have more than one mode)
Median - Put in order, pick out the middle number
Example
6, 3, 4, 8, 2 put in order 2, 3, 4, 6, 8
Median = 4
Range - The difference between the maximum and minimum.
(maximum – minimum)
Example
Find the range of the following
16
42
17
31
41
37
Maximum number = 42
Minimum number = 16
Range
= 42 – 16 = 26
Workbook 15
Level 2 Numeracy/Application of Number
2
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
Heights of 5 people
170 cm
182 cm
184 cm
190 cm
190 cm
63 kg
56 kg
84 kg
Weights of 7 people
54 kg
72 kg
56 kg
91 kg
Exercise 1
1.
Find the modes in the lists of data above.
2.
Find the medians in the lists of data above.
(N.B. If there are two numbers in the middle add them together and divide by 2)
3.
Find the range in the lists of data above.
Workbook 15
Level 2 Numeracy/Application of Number
3
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
Pictogram of Shoe Sizes






Frequency
6
5
4
3
2
1


 
  
   
4
5
6
7




9
10
11
8
Shoe Size
A survey of 21 people buying shoes was conducted. The sizes which they bought were as
follows:-
8
5
9
6
7
8
7
4
6
6
5
11
9
7
10
7
8
7
8
8
8
Information in this form is known as RAW DATA.
Workbook 15
Level 2 Numeracy/Application of Number
4
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
Exercise 2
If you completed the frequency chart and bar chart at Level 1 look back at those
charts.
1.
Copy and complete the following FREQUENCY CHART
Shoe size
Tally
Frequency
4
5
6
7
8
9
10
11
Total
Workbook 15
Level 2 Numeracy/Application of Number
5
21
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
2.
Draw a bar chart from the information you have in your Frequency Table
Shoe size is your horizontal axis (4 to 11) and frequency is your vertical axis (0 to 6).
The shoe size with the highest frequency is the MODE. The shoe size with the highest bar
on your Bar Chart is also the MODE
To work out the MEDIAN of all the shoe sizes from the raw data put in order, the smallest
first.
The MEDIAN is now the middle one (ie the eleventh one) 4, 5, 5, 6, 6, ...
The RANGE is the largest shoe size minus the smallest shoe size.
To work out the MEAN, first add up all the shoe sizes from the raw data, then divide this
by the number of people in the survey (i.e. divide by 21 in this case).
Workbook 15
Level 2 Numeracy/Application of Number
6
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
An alternative method of calculating the MEAN is to use the frequency table.
3.
Copy and complete this amended table.
Shoe size (s) Frequency (f)
s×f
4
5
2
5×2=
10
6
7
8
9
10
11
Totals
21
The MEAN is calculated by dividing the total of the s  f column by the total of the Frequency
column (i.e. 21)
MEAN =
4.
?
21
Find the mean, median, mode and range from the shoe size survey.
Workbook 15
Level 2 Numeracy/Application of Number
7
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
Exercise 3
Measure the height of each member of a group (e.g. family, colleagues or class). Ask your
tutor to set limits for the data.
1.
find the mean and mode and draw a bar graph for the whole group.
2.
find the mean and mode and draw a bar graph for females.
3.
find the mean and mode and draw a bar graph for males.
4.
find the range.
Workbook 15
Level 2 Numeracy/Application of Number
8
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
This is an example of a line graph with more than 1 line
Weight loss chart
80
79
Weight (kg)
78
77
Pat
Jane
76
75
74
73
72
1-Jan
8-Jan
15-Jan
22-Jan
29-Jan
5-Feb
Date
Exercise 4
1.
Pat was heavier than Jane on Jan 1, by how much? ……….kg
2.
How much weight did Pat lose in total? ……….kg
3.
Jane stayed the same for 2 weeks. How much did she weigh then? …….kg
4.
What was Jane’s weight on Feb 5? ………kg
Line graphs represent continuous data. Continuous data is something you can measure,
which changes over a period of time, e.g. a child’s height, the exchange rate of £ sterling.
5.
Check the maximum temperature for Edinburgh and London in the daily newspaper
every day for a week.
Draw a graph to show how temperature changes in both cities over the week.
[Both cities on one graph]. Make sure that you add a suitable title and labels.
Workbook 15
Level 2 Numeracy/Application of Number
9
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
Exercise 5
1.
Using a protractor, work out the angle which represents the following:
a. 50% =
°
b. 25% =
°
c. 45% =
°
d. 30% =
°
e. 60% =
°
Workbook 15
Level 2 Numeracy/Application of Number
10
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Statistics
HD1/L2.1-4
In order to calculate the angle, first of all you need to know the percentage and then find that
percentage of 360
[You may need to look back at Workbook 7 – Percentages]
e.g.
To show 50%
50% of 360
=
50
× 360 = 180
100
To show 30%
30% of 360
=
2.
3.
30
× 360 = 108
100
Work out the following, then check them on the percentage dial
a)
25% =
°
b)
40% =
°
c)
60% =
°
d)
10% =
°
e)
75% =
°
Check the shoe size of 20 friends or colleagues. Use a tally chart to organise the data
into sensible ranges, and record their answers.
Calculate the percentage of people in each size range and create a pie chart. Show all
workings out.
Be careful to make sure that you label the chart clearly.
Workbook 15
Level 2 Numeracy/Application of Number
11
© West Nottinghamshire College 2004