DescriptiveDescriptiveStatisticsStatistics

Advanced Higher GeographyAdvanced Higher Geography

Ollie Bray – Knox Academy, East Ollie Bray – Knox Academy, East LothianLothian

Descriptive statistics Descriptive statistics include:include:

Types of dataTypes of data

Measures of central tendencyMeasures of central tendency

Measures of dispersionMeasures of dispersion

Types of data (1)Types of data (1)

Nominal data:Nominal data: data that has names. data that has names. eg: rock types (sedimentary, igneous eg: rock types (sedimentary, igneous or metamorphic).or metamorphic).

Ordinal data:Ordinal data: data that can be data that can be placed in ascending or descending placed in ascending or descending order. eg: settlement type (city, order. eg: settlement type (city, town, village & hamlet).town, village & hamlet).

Types of data (2)Types of data (2)

Interval data:Interval data: data with no true data with no true zero. Very uncommon so don’t worry zero. Very uncommon so don’t worry about it.about it.

Ratio data:Ratio data: most numerical data. most numerical data.

Central TendencyCentral Tendency

When you calculate the central When you calculate the central tendency of a data set you calculate tendency of a data set you calculate its its averageaverage..

The measurements used for The measurements used for calculating central tendency include calculating central tendency include the the meanmean, the , the modemode and the and the medianmedian..

The MeanThe Mean Calculating the mean is one of the Calculating the mean is one of the commonly used statistics in geography. commonly used statistics in geography.

It is found by totalling the values for all It is found by totalling the values for all observations (∑x) and dividing by the observations (∑x) and dividing by the total number of observations (n).total number of observations (n).

The formula for findingthe mean is:

Mean = ∑x n

The MedianThe Median

The median is the middle value when The median is the middle value when all of the data is placed in all of the data is placed in ascending / descending order.ascending / descending order.

Where there are two middle values Where there are two middle values we take the average of these.we take the average of these.

The ModeThe Mode

The mode is the number that occurs The mode is the number that occurs the most often.the most often.

Sometimes there are two (or more) Sometimes there are two (or more) modes. Where there are two modes modes. Where there are two modes the data is said to be bi-modal.the data is said to be bi-modal.

Find the mean, median and mode of Find the mean, median and mode of the following data.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

Mean5

Mode4

Median4

5 mins©Microsoft Word clipart

Groups of dataGroups of data

Sometimes the data we collect are in Sometimes the data we collect are in group form.group form.

Finding the Finding the meanmean is slightly more difficult. is slightly more difficult. We use the midpoint of the group and We use the midpoint of the group and multiply this by the frequency.multiply this by the frequency.

Slope Angle Slope Angle ((°)°)

Midpoint (x)Midpoint (x) Frequency (f)Frequency (f) Midpoint x frequency (fx)Midpoint x frequency (fx)

0-40-4 22 66 1212

5-95-9 77 1212 8484

10-1410-14 1212 77 8484

15-1915-19 1717 55 8585

20-2420-24 2222 00 00

TotalTotal n = 30n = 30 ∑∑(fx) = 265(fx) = 265

Slope Angle Slope Angle ((°)°)

Midpoint Midpoint (x)(x)

Frequency Frequency (f)(f)

Midpoint x frequency Midpoint x frequency (fx)(fx)

0-40-4 22 66 1212

5-95-9 77 1212 8484

10-1410-14 1212 77 8484

15-1915-19 1717 55 8585

20-2420-24 2222 00 00

TotalTotal n = 30n = 30 ∑∑(fx) = 265(fx) = 265

The mean is: ∑(fx)/n =265 / 30 = 8.8

Which is in the 5 – 9 group

Slope Angle Slope Angle ((°)°)

Midpoint Midpoint (x)(x)

Frequency Frequency (f)(f)

Midpoint x frequency Midpoint x frequency (fx)(fx)

0-40-4 22 66 1212

5-95-9 77 1212 8484

10-1410-14 1212 77 8484

15-1915-19 1717 55 8585

20-2420-24 2222 00 00

TotalTotal n = 30n = 30 ∑∑(fx) = 265(fx) = 265

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 turnYour turn

Read page 25 – 29 of ‘Geographical Read page 25 – 29 of ‘Geographical Measurements and Techniques: Measurements and Techniques: Statistical Awareness, LT Scotland, Statistical Awareness, LT Scotland, June 2000. June 2000.

Answer questions 1 & 2 from Task 4 Answer questions 1 & 2 from Task 4 in this book.in this book.