Maths + Stats Flashcards
Bivariate Data
Data with 2 variables
Basically scatter graphs
What can we plot?
Socio-economic data - global and local Physical data - rivers and hydrology Fieldwork data - beefed up in new curriculum
What can students use Gapminder for?
Students can use the tools to create can scatter graph easily.
Students can use it for homework.
Positive correlation
As one goes up so does the other.
Negative correlation
As one increases the other decreases.
No correlation
No relationship, connection, or interdependence between the two variables.
How to describe the strengths of the correlation?
Strong vs Weak
Trend lines
- Drawn on by hand
- Illustrates general pattern that the graph shows
- Bigger picture of data
Line of Best Fit
- In exam they will be expected to draw this on to a graph.
- Shows the pattern
strong / weak positive/negative correlation. - Same number of points above and below the line
- Doesnt need to go through origin
Clusters
Are their clusters of data?
- What does that show?
e. g. Low/emerging/high income countries clustered together?
Anomalies
Data points not in the clusters / far from the other data.
Think why?
- What country is it?
- What are they doing differently?
What to remember about correlation?
Correlation does not equal causation.
Interpolate
Finding the value between two other values.
Extrapolate
Beyond what is on the graft and make a prediction.
Central Tendency
The tendency for the values of a random variable to cluster round its mean, mode, or median.
Spread
That is a measure the variability of values in a sample or the range.
Cumulative Frequency
This is a running total of frequency up to that point.
- Add the numbers of frequency up as you go through the data/table
- Can present as a cumulative frequency graph
Dispersion Diagrams
- Simple but students struggle.
- Show spread or range within one or possibly 2 sets of data.
- Visual way to see the degrees of dispersion or clustering of data.
How to plot a dispersion diagrams?
- Work out axis
For each time in the sample: - Plot where it occur on your Y axis
- If they have the same data they will appear in a row at that number
How can dispersion diagrams help us?
- Show us range
- Show us cluster
- Easy to see/calculate mean, mode, median
- Starting point for calculating inter-quartile range
Range
largest value minus smallest value
NB: It is the range of the data values, not of the frequencies.
A larger range means the data is less consistent. A smaller range means the data is
more consistent.
Mean
Add up all the values and divide by the number of values in the sample.
Mode
Most frequently occuring value.
Median
Middle value when in rank order.
Interquartile Range
- Divide data into 4 equal groups or quartiles
- Difference between the boundary of the one upper and lower quartile
- Show spread and distribution around the median
Upper Quartile
Number in the sample +1 divided by 4 = rank position for upperquartile
e.g. (11+1) /4 = 3rd highest value (count down 3 data points from the top)
Lower Quartile
3 x (number in the sample plus 1) divided by 4 = rank position
e.g. 3x(11+1) / 4 = 9th highest value (count down 9 data point from the top)
Modal class
Groups of data
= most frequently occurring group
Can use dispersion diagrams for?
- Variation of population by continent
- Rainfall in an area or between places
- Traffic counts between locations of times
- Socio-economic data
- Use in fieldwork
Think about how you will collect and plot data from fieldwork
Why is GIS useful?
- Geospatial/geolocated
- Visualise
- Interpret - explain sata
- Explore - enquire and ask questions about the data by adding or removing layers
- Patterns - distributions, concentrations, anomalies
- Connections
- Trends
GIS we can use in school?
Google earth
- Free
- Simple
- Not easy to add own data
ArcGIS
- Free
- Used by FSC
- Add own data
Police.org website
Environment agency
Digimaps
London air quality nowcast maps
GIS in fieldwork
Could use it to layer the data they got onto other layers
Research places before you go
- Risk assessment
Data collection
- Looking at relief and altitude , distances?
Data analysis and presentation
- Desire lines or flow lines onto the map
Bi-modal
Has 2 modes
Qualitative
Descriptive data
More subjective
Quantitative
Numerical data
Can be measured precisely
Discrete and continuous data
Discrete - only certain values according to context - whole numbers/ shoe sizes etc (in Geog can be known as discontinuous data)
Continuous - is measured - can take any value
Categorical Data
No numerical data but can still be sorted into groups e.g. preferences from an interview.
Bar Chart
- Can show qualitative or quantitative, discrete or continuous data.
- Frequency is usually shown on the vertical axis (but can be on the horizontal axis
with the bars in the chart shown horizontally). - should be equal width
- Gaps between bars (unless continuous data)
Bar-line chart
Same as a bar chart but instead of a bar it is one thin line going up where the bar would be
Frequency Diagram
Another name for a bar chart where the vertical axis is labelled frequency.
Comparative Bar Chart
Compares 2 or more sets of data using different coloured bars (needs a key).
Compound bar chart
Combines different sets of data in one bar. (needs key for colours)
Histogram
Bar chart for continuous data.
No gaps between bars
Pie chart
The angle of each sector is proportional to the
number of items in that category
Shows proportions of a set of data, e.g. fraction or
percentage of waste recycled
Scatter graph
A scatter graph plots two sets of data on the same graph to see if there is a
relationship or correlation between them.
Scatter graphs can show positive, negative or no correlation.
Plotted with crosses.
Independent variable goes on which axis?
Horizontal axis
Line graph can show?
Trends in data. The trend is the general direction of change,
ignoring individual ups and downs.
Proportional relationships on graphs
- direct proportion
A straight line graph through the origin (0, 0) shows that the two variables are in
direct proportion.
When one variable doubles, so does the other. When one halves, so does the other.
The relationship is of the form y = mx, where m is the gradient of the graph.
Proportional relationships on graphs
- linear realtionship
A straight line graph not through the origin.
The relationship is of the form y = mx + c, where m is the gradient of the graph and
c is the y-intercept (where the graph crosses the y-axis).
Fractions
- Write fractions on two lines, not on one line.
- Avoid ‘cancelling’ – instead, write fractions in their simplest form.
- In a fraction, the horizontal line means ‘divide’.
- A ‘dot’ over a decimal value shows the number recurs
- A dot over two decimal values shows the numbers between the dots recur, e.g.
0.1̇5̇ means 0.151515… and 0.24̇751̇ means 0.247514751… - The reciprocal of a number is 1 ÷ the number. For fractions, this means the
reciprocal of a/b= 1 ÷ a/b
= 1 × b/a =b/a - Dividing by a fraction is the same as multiplying by its reciprocal.
Percentage
- Percent means ‘out of 100’. A percentage is a fraction with a denominator of 100.
- You can calculate percentages of amounts, e.g. 20% of $500.
- You can write one number as a percentage of another, e.g. write 7/50 as a percentage.
How to calculate an irregular shape?
e.g. river catchment
- draw round
the shape on graph paper that has small squares. - count the squares inside the
area.
For squares that cross the perimeter, count those that are more than half-in as
whole ones, and don’t count those that are more than half-out. This will give you an
estimate of the area.
(The smaller the graph squares, the more accurate the estimate)
Remember that area is measured in square units, such as km2, m2 or cm2
.
Calculate area of rectangle
Area of a rectangle = length × width
Calculate area of triangle
This formula works for all triangles, not just right-angled ones.
h is the perpendicular height (90 degree measurement from base to highest point).
Area of triangle = 1/2 (0.5) × base × height
Surface area of cuboid
Draw the net
Work out each face (side)
- width x length for each face of the cuboid
Add together all the face measurements
3d shape masurements
3-D shape is the amount of space it takes up. It is measured in cubed units - mm3, cm3, m3
Capacity is the amount of liquid a 3-D solid can hold. It is measured in ml or litres.
Measurement conversions
1000 Metres = 1km (in straight line)
In area:
1 hectare = 10,000 m2 (100m by 100m box)
100 hectrares - 1km2
20 ha = 200,000m2
1 cm3 = 1 ml.
Standard Form
A way of writing very large or very small numbers as a number
between 1 and 10 multiplied by a power of 10.
4000 = 4 x10(superscript3)
Decimals - superscript is minus (eg -3)
