1. How could data be used in an EPQ?
Nicholas Martindale
4th November 2017

2. Aims To help students feel confident in using data.
To help students use and present data effectively.

3. Questions What is data? What questions can we ask with data?
How can we use data to answer these questions?

4. 1. What is data?
A collection of facts or values which can be processed to provide information.
Variables
Observations

5. 1. What is data?
A collection of facts or values which can be processed to provide information.
Numerical Variables
(e.g. counts, percentages)
Categorical Variables
(e.g. names, groups)

6. 2. What questions can we ask with data?
Representative value: What is a typical value? Spread: How much variation is in the data? Composition: What’s in the data? Distribution: The shape of the data. Comparison: Differences between groups. Trend: Change over time. Relationship: How one thing depends on another.
Summarising data
Presenting data

7. 3. Answering questions: summaries
Representative value: What is a typical value? Spread: How much variation is in the data? Composition: What’s in the data? Distribution: The shape of the data. Comparison: Differences between groups. Trend: Change over time. Relationship: How one thing depends on another.
Summarising data
Presenting data

8. 3. Answering questions: summaries
Representative value: what is a typical value?
A typical value can help us summarise a large amount of data with a single representative number.
e.g.
The mean number of students in primary schools is 271
There are different representative values you could choose from.

9. 3. Answering questions: summaries
Representative value: what is a typical value?
Measure of Centre
Definition
Advantages
Disadvantages
Examples
Mean
Sum of values / Total number of values
Very familiar.
Uses all the data.
Very large/small values can distort the answer.
( ) / 3 = 2
( ) / 3 = 12
Median
Middle value when in order
Not affected by very. large/small values.
Only depends on the middle values so may not be representative.
1, 2, 3 : median = 2
1, 2, 33: median = 2
0, 0, 0, 0, 0, 0, 2, 9, 9, 9, 9, 9, 9
median = 2
Mode
Most common value
The only average that can be used with non-numerical data.
There may be no mode.
There may be more than one mode.
1, 2, 3 : no mode
1, 2, 2, 3: mode = 2

10. 3. Answering questions: summaries
Spread: how much variation is in the data?
A measure of spread can help us summarise how much the data varies or how unequal it is.
e.g.
The range of number of students in primary schools is 1455 – 5 = 1450.
There are different measures of spread you could choose from.

11. 3. Answering questions: summaries
Spread: how much variation is in the data?
Measure of Spread
Definition
Advantages
Disadvantages
Range
Largest – Smallest
Easy to calculate.
Familiar to students.
Not very informative.
Distorted by very large/small values.
Does not use all the data.
Interquartile Range
Upper Quartile – Lower Quartile
Not distorted by extreme values.
Standard Deviation
Mean distance of each value from the overall mean
Statistically sophisticated.
Calculated in Excel/Google/R.
Unfamiliar to students.
Inappropriate for skewed data.

12. 3. Answering questions: summaries
Representative value: What is a typical value? Spread: How much variation is in the data? Composition: What’s in the data? Distribution: The shape of the data. Comparison: Differences between groups. Trend: Change over time. Relationship: How one thing depends on another.
Summarising data
Presenting data

13. 3. Answering questions: advice on figures
What advice do students need on the use of figures?

14. 3. Answering questions: advice on figures
How to present figures:
Where to put figures:
Think first about what you want
Soon after they are referred to in the text.
to show, then choose a graph.
- Text size and font easy to read.
How to refer to figures:
- Appropriate, informative title.
- All figures should have a reference number e.g. “Figure 2”
- Clearly labelled axes including units.
- All figures used should be referred to in the text e.g. “see Figure 2”
Clearly labelled data (groups).
Keep them uncluttered.

15. 3. Answering questions: presenting data
Which type of figure we use depends on the type of question we are trying to answer:
Type of Question
Recommended Types of Figure
Composition:
What’s in the data?
Counts: Bar Chart
Proportion: Pie Chart
Distribution:
What’s the shape of the data?
Histogram
Boxplot
Comparison:
Differences between groups
Side-by-Side Bar Chart
Side-by-Side Boxplot
Trend:
Changes over time
Counts: Line graph, Multiple Bar Chart
Distribution: Multiple Boxplots
Relationship:
How one thing depends on another
Scatterplot

16. 3. Answering questions: composition
What’s in the data? We might want to show counts or proportions. Counts  Bar Charts Proportions  Pie Charts

17. 3. Answering questions: composition
Counts: Bar Chart
Include 0 on the
y-axis so that you
don’t mislead the
reader.

18. 3. Answering questions: composition
What’s wrong here?

19. 3. Answering questions: composition
Make sure to include 0 on the y-axis so that you don’t mislead the reader.

20. 3. Answering questions: composition
Proportions Pie Chart - Include percentage labels.
2.0%
3.4%
26.7%
68.0%

21. 3. Answering questions: composition
What’s wrong here?

22. 3. Answering questions: composition
The perspective in 3D distorts
our perception of the relative sizes
of the sectors.
Avoid using 3D plots, they are
often misleading.

23. 3. Answering questions: distribution
What’s the shape of the data?  Boxplots  Histograms

24. 3. Answering questions: distribution
Boxplot
50% of schools have a PTR of less (or more) than 19 (median = 19).
25% of schools have a PTR of 17 or less (lower quartile = 17)
- 25% of schools have a PTR of 22 or more (upper quartile = 22)
- All schools except outliers have a PTR between 8 and 31 (range of whiskers).
Lower
Quartile
Upper Quartile
Median

25. 3. Answering questions: distribution
Histogram
- Same data as boxplot.
Data is roughly symmetrical around 20.
The mode PTR is about 20.
There are very few schools with PTR less than 10 or greater than 30.
Mode

26. 3. Answering questions: distribution
Skewed Data: when the data is not symmetrical Left Skew (long left tail) Right Skew (long right tail)

27. 3. Answering questions: comparison
How do groups in the data differ? Counts/Proportions  Side-by-Side Bar Charts Distributions  Side-by-Side Boxplots

28. 3. Answering questions: comparison
Side-by-Side Bar Charts Side-by-Side Boxplots

29. 3. Answering questions: trend
How does the data change over time? We might want to show how counts, proportions or distributions change over time. Counts  line graphs, multiple bar charts Proportions  stacked bar graphs Distributions  multiple boxplots

30. 3. Answering questions: trend
Counts over time: Line Graph

31. 3. Answering questions: trend
Proportions over time:
Stacked Proportion Bar Chart
Each bar represents all
schools in a given year.
The proportion of each
type of school is represented
by its height within the bar.

32. 3. Answering questions: trend
Distributions over time: Multiple Boxplots
The median is increasing,
so the typical school is
growing larger over time.
The interquartile range
is increasing, so the difference in
size between smaller and larger schools is increasing.

33. 3. Answering questions: relationship
Does the value of one variable depend on another? - We’ve already seen cases where the value of a numerical variable depends on the value of a categorical variable i.e. - % teachers over 50 depends on the type of school. - Number of schools depends on the phase and the type of school.

34. 3. Answering questions: relationship
Does the value of one variable depend on another?
When we want to check if one numerical variable depends on the value of another numerical variable we check to see if they is a correlation between them.
We use scatterplots to visually assess the relationship between two variables.

35. 3. Answering questions: relationship
Does the value of one variable depend on another?
The value of a correlation is defined as being between -1 and 1.
This “correlation coefficient” can be calculated easily in Excel or Google Sheets.

36. 3. Answering questions: relationship
Positive Correlation
Correlation coefficient = 0.7
As the PTR increases the % of pupils achieving 5 A*-C also increases

37. 3. Answering questions: relationship
Negative Correlation
Correlation coefficient = -0.8
As the % FSM increases the % of pupils achieving 5 A*-C decreases.

38. 3. Answering questions: relationship
No Correlation (or very little)
Correlation coefficient = 0.06
There doesn’t seem to be a relationship between the % male teachers and the % 5 A*-C

39. Conclusion How to use data depends on the question being asked.
Type of Question
Recommended Use of Data
Representative Value:
What’s a typical value?
Mean, Median, Mode
Spread:
How much variation is in the data?
Range, Interquartile Range, Standard Deviation
Composition:
What’s in the data?
Counts: Bar Chart
Proportion: Pie chart
Distribution:
What’s the shape of the data?
Histogram
Boxplot
Comparison:
Differences between groups
Side-by-Side Bar chart
Side-by-Side Boxplot
Trend:
Changes over time
Counts: Line graph, Multiple Bar chart
Distribution: Multiple Boxplots
Relationship:
How one thing depends on another
Scatterplot
How to use data depends on the question being asked.