Statistics, graphs and maps

Question 1

Measures of central tendency methodology (mean, median and mode)

Answer 1

1. Tells us the middle point in a set of data
2. Mode is the number that appears most often in a set of data
3. Median is the middle point in a sorted list of numbers from low to high. If there are an even amount of numbers in the set then the median is the mean of the two middle numbers
4. Mean is calculated by adding all the numbers in a set up and dividing by how many there are

Question 2

Measures of central tendency considerations and limitations

Answer 2

Outliers have large effect on the mean and can throw off an average if a data set

Question 3

Measures of dispersion methodology (range and IQR)

Answer 3

1. Tells us spread of data around a central value
2. Range is the maximum minus the minimum value on a data set
3. The interquartile range (IQR). A quartile is one of three point that divide a range of data into four equal parts. Each quartile is 25%. The IQR is the difference between Q3 and Q1. IQR = Q3 - Q1. Less sensitive to outliers.

Question 4

Measures of dispersion considerations and limitations

Answer 4

Normal distribution is assumed

Question 5

Chi-squared analysis advantages and disadvantages

Answer 5

Advantages:
1. Can test associations between variables
2. Useful in measuring the differences between observed and predicted data
3. Useful when data can be grouped into classes
4. Chi-squared value can be compared to significance tables
Disadvantages:
1. Cannot use percentages
2. Data must be in the form of frequencies
3. Number of observations must be more than 20
4. Difficult formula so fairly complicated and time consuming to get right

Question 6

Chi-squared analysis definition

Answer 6

Used to compare observed data with data we would expect to obtain according to a specific hypothesis

Question 7

Spearman rank correlation coefficient purpose

Answer 7

Measures strength and direction of a relationship between 2 variables

Question 8

Spearman rank correlation coefficient considerations and limitations

Answer 8

1. Extreme values won’t effect result
2. Fairly quick and easy to calculate if data set isn’t too large
3. Only tests linear relationship
4. Can be time consuming if data set is large
5. Pearson’s tends to be more accurate as it uses actual ,rather than ranked, values

Question 9

Pearson product moment correlation coefficient (PPMCC) purpose

Answer 9

Measures strength of a linear relationship between two variables

Question 10

Pearson product moment correlation coefficient considerations and limitations

Answer 10

1. Uses actual values rather than ranks so more accurate and reliable than Spearman’s when drawing conclusions
2. Differences between values in the data set are taken into account so more accurate than ranking
3. Larger, more tedious and more complicated than Spearman’s
4. Assumes that the data had normal distributions
5. Affected by extreme values

Question 11

Linear regression (best fit line on scatter graph) purpose

Answer 11

To determine the linear relationship between one dependent variable and one independent variable

Question 12

Linear regression considerations and limitations

Answer 12

1. Allows accurate best fit line to be drawn
2. More accurate than drawing best fit line by eye or your own judgement
3. Cannot be used for non-linear relationships
4. Time consuming and complicated to carry out due to using a complicated mathematical formula rather than arithmetical calculations

Question 13

Nearest neighbour analysis purpose

Answer 13

Used to measure distributions according to where they are clustered, random or regular

Question 14

Nearest neighbour analysis considerations and limitations

Answer 14

1. Better than a visual observation which can be subjective
2. Allows you to compare distribution of either 2 similar or 2 different areas
3. Need a minimum of 30 points
4. Large number of points can make the calculation tedious and time consuming
5. Doesn’t take other controlling factors into account e.g natural resources

Question 15

Bipolar analysis purpose (EQS)

Answer 15

Used to compare areas, people or gathered data

Question 16

Bipolar analysis advantages and disadvantages

Answer 16

+visual, patterns identified easily
+can compare lots of diff aspects on same graph
- can become cluttered if too many areas are compared
- results are based on people’s perceptions which may be biased

Question 17

Dispersion diagram purpose (test tube with dots)

Answer 17

Shows the range of a group of drama and their tendency to group or disperse

Question 18

Dispersion diagram advantages and disadvantages

Answer 18

+ shows spread from the mean
+ patterns and anomalies easily stand out
+ other calculations can be made e.g. mean, mode, median and range
+ can calculate standard deviation
- can become easily crowded when more than one thing has the same value
- further statistical analysis requires as the spread does not tell you everything about a set of data

Question 19

Kite diagrams purpose

Answer 19

Shows density and distribution of vegetation or species along a transect

Question 20

Kite diagrams advantages and disadvantages

Answer 20

+ useful for displaying changes over a distance
+ patterns and trends are made clear
- calculating a % to put on the diagram can be difficult
- time consuming to plot

Question 21

Logarithmic graph purpose

Answer 21

Used when values on a scale are too large to show on linear graph paper (increases by multiplication rather than addition)

Question 22

Logarithmic graphs advantages and disadvantages

Answer 22

+ allows you to plot data that greatly differs in size on the same graph
+ can easily see patterns between values which would have been hard to see from raw data alone
- complicated to draw to appropriate scale
- complicated to read
- if changes are small they can be hard to see, particularly with higher values
- difficult to plot values accurately
- time consuming to draw

Question 23

Polar graphs purpose

Answer 23

Used to show direction as well as magnitude

Question 24

Polar graph advantages and disadvantages

Answer 24

+ directions can be seen clearly, very visual
+ info from different variables on the same graph
+ quick to read
+ quick to draw IF given a template
- hard to draw a suitable scale
- hard to draw concentric circles
- time consuming without template
- can become cluttered in the middle
- if there are huge variations in the data the circle may be huge

Question 25

Systems diagram purpose (water cycle)

Answer 25

Simplified diagrams that can be used to convey complex relationships

Question 26

Systems diagram advantages and disadvantages

Answer 26

+ visual - easier than large body of text + connections can be sen clearer - big picture - complicated if something fits in more than 1 place - time consuming and complicated to draw

Question 27

Scatter graph purpose

Answer 27

Used to show relationship or correlation between 2 variables

Question 28

Scatter graph advantages and disadvantages

Answer 28

+ can plot bets fit line to see overall trend + visual + fairly quick and straightforward to plot + large amounts of data can be put on 1 graph + anomalies stand out - can only display 2 variables - mistakes can easily be made if large amounts of data needs to be plotted - further statistical analysis always necessary

Question 29

Triangular graphs purpose

Answer 29

Used to show data that can be divided into three parts

Question 30

Triangular graphs advantages and disadvantages

Answer 30

+ can show 3 variables on the same graph + can display large amounts of data in the same place + dominant characteristics can be easily identified + clusters emerge allowing trends to be identified - data has to be presented as a percentage % - complicated and time consuming to read and plot

Question 31

Choropleth map advantages and disadvantages

Answer 31

+ allows for easy visual comparison between areas + can show lots of info at a time + easy to draw + grouping the data makes it fairly straightforward to accommodate a range of values - uses average so doesn’t show a true picture of an area - boundaries give impression of marked changes where in reality the changes may be more gradual

Question 32

Proportional symbol map advantages and disadvantages

Answer 32

+ differences can be seen at a glance + large amounts of data can be summarised in visual form + patterns and trends can be easily identified + a key can be used for actual figures so map doesn’t become cluttered - scale has to be carefully considered (symbols can’t be so big they overlap or so small they can’t be read) - size of symbols can mean precise locations are obscured - time consuming to draw

Question 33

Dot map advantages and disadvantages

Answer 33

+ more specific than choropleth map as it doesn’t use averages + comparisons between different areas can be made easily + lots of different things can be displayed + visual - patterns, trends, distributions and densities can all be seen clearly + data for exact locations can be pinpointed - too many dots can clutter the map and make it hard to read - accurate scale can be difficult to find (dots aren’t too big or small) - time consuming to plot if there’s lots of data over a large area - if dots are evenly spread out this can give a false impression that the distribution is the same across a whole area

Question 34

Flow line map advantages and disadvantages

Answer 34

+ links between places can be seen clearly + volume and direction of movement is clear + thickness of lines allows you to compare data from different areas + patterns and trends can be spotted + can show a variety if different movements e.g people or goods - base map must be very basic and minimal - time consuming to construct - can be hard to find suitable scale for thickness of arrows - careful planning required so lines don’t cross or obscure each other

Question 35

Sphere of influence map advantages and disadvantages

Answer 35

+ allows you to show visually where people come from to use a shop or service + can work out distances allowing you to make comparisons with other places + let’s you compare differences e.g SOI in shopping centre on the outskirts v CBD - can be harder to draw in densely populated areas - physical barriers like rivers and mountains aren’t taken into account - time consuming

Question 36

Isoline map advantages and disadvantages

Answer 36

+ allows you to join together areas with the same data thus establishing links between them + gradual patterns can be seen clearly across a large area + uses fixed intervals so changes can be easily identified - random values in the middle of similar data can make isolines hard to draw - requires large amount of data for lots of different locations - can be difficult to know where isolines go if you have small amounts of data in an area

Question 37

Cross section advantages and disadvantages

Answer 37

+ let’s you look at one specific part of an area + good visual overview of the area under study + can be compared with other area easily - can be very difficult to draw especially if contour lines are very close together - sometimes it can be difficult to see exactly where contours are e.g. in wooded areas

Question 38

Transect advantages and disadvantages

Answer 38

+ let’s you focus on a specific area - manageable + can compare land use along a transect + can allow overview for comparison - if regeneration has taken place it can be hard to compare transect to urban models - difficult to incorporate a wide variety of land uses into one single straight line transect so multiple may need to be carried out