Download Descriptive Statistics

Advanced Higher Geography
Descriptive
Statistics
Ollie Bray – Knox Academy, East Lothian
Descriptive statistics include:
Types of data
Measures of central tendency
Measures of dispersion
Types of data (1)
Nominal data: data that has names. eg:
rock types (sedimentary, igneous or
metamorphic).
Ordinal data: data that can be placed in
ascending or descending order. eg:
settlement type (city, town, village &
hamlet).
Types of data (2)
Interval data: data with no true zero.
Very uncommon so don’t worry about it.
Ratio data: most numerical data.
Central Tendency
When you calculate the central
tendency of a data set you calculate its
average.
The measurements used for calculating
central tendency include the mean, the
mode and the median.
The Mean
Calculating the mean is one of the
commonly used statistics in geography.
It is found by totalling the values for all
observations (∑x) and dividing by the
total number of observations (n).
The formula for finding
the mean is:
Mean = ∑x
n
The Median
The median is the middle value when all
of the data is placed in ascending /
descending order.
Where there are two middle values we
take the average of these.
The Mode
The mode is the number that occurs the
most often.
Sometimes there are two (or more)
modes. Where there are two modes the
data is said to be bi-modal.
5 mins
©Microsoft Word clipart
Find the mean, median and mode of the
following data.
The weekly pocket money for 9 first year pupils was
found to be:
3 – 12 – 4 – 6 – 1 – 4 – 2 – 5 – 8
Mean
5
Median
4
Mode
4
Groups of data
Sometimes the data we collect are in
group form.
Slope Angle (°)
Midpoint (x)
Frequency (f)
Midpoint x frequency (fx)
0-4
2
6
12
5-9
7
12
84
10-14
12
7
84
15-19
17
5
85
20-24
22
0
0
n = 30
∑(fx) = 265
Total
Finding the mean is slightly more difficult. We
use the midpoint of the group and multiply this
by the frequency.
Slope Angle (°)
Midpoint (x)
Frequency (f)
Midpoint x frequency (fx)
0-4
2
6
12
5-9
7
12
84
10-14
12
7
84
15-19
17
5
85
20-24
22
0
0
n = 30
∑(fx) = 265
Total
The mean is: ∑(fx)/n = 265 / 30 = 8.8
Which is in the 5 – 9 group
Slope Angle (°)
Midpoint (x)
Frequency (f)
Midpoint x frequency (fx)
0-4
2
6
12
5-9
7
12
84
10-14
12
7
84
15-19
17
5
85
20-24
22
0
0
n = 30
∑(fx) = 265
Total
We cannot find the mode for grouped data but
we can find the modal group. The modal group.
The modal group is the group that occurs most
frequently (ie: 5-9 group).
Your turn
Read page 25 – 29 of ‘Geographical
Measurements and Techniques:
Statistical Awareness, LT Scotland,
June 2000.
Answer questions 1 & 2 from Task 4 in
this book.