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.

Task Answers Find the mean, median and mode of the following data. 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 Answers Mean 5 Median 4 Mode 4

Midpoint x frequency (fx) 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 84 10-14 15-19 17 5 85 20-24 22 Total n = 30 ∑(fx) = 265 Finding the mean is slightly more difficult. We use the midpoint of the group and multiply this by the frequency.

Midpoint x frequency (fx) Calculating the mean Slope Angle (°) Midpoint (x) Frequency (f) Midpoint x frequency (fx) 0-4 2 6 12 5-9 7 84 10-14 15-19 17 5 85 20-24 22 Total n = 30 ∑(fx) = 265 The mean is: ∑(fx)/n = 265 / 30 = 8.8 Which is in the 5 – 9 group

Midpoint x frequency (fx) Calculating the mode Slope Angle (°) Midpoint (x) Frequency (f) Midpoint x frequency (fx) 0-4 2 6 12 5-9 7 84 10-14 15-19 17 5 85 20-24 22 Total n = 30 ∑(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 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. 10 mins