1. Using your knowledge to describe the features of graphs
Describing Graphs
Using your knowledge to describe the features of graphs

2. For each sample make descriptive statements about- - Spread - Shape - IQR
Describing

3. Spread You should ask yourself about how the data is spread out:
What is the range?
What is the IQR?
How big is the IQR compared to the range?
Are the quarters even?
You should be able to describe the situation using correct terminology.
Spread

4. Generally we compare the data to a normal distribution (pictured below)
Shape

5. To get an idea of shape you can sketch a rough outline of your distribution.
Is the data grouped in certain locations?
Is the data unimodal (is there one clear peak)?
Is the data skewed?
Shape

6. Skew- always describe the tail!
Shape

7. BOYS1 Spread? Shape?

8. BOYS2 Shape? Spread?

9. BOYS3 Spread? Shape?

10. Inter-Quartile Range IQR is the middle 50% of the data-
Its the box in the box and whisker plot!
When we compare two subsets we need to compare the IQR’s to make a decision about differences in the population.
If there is a significant separation we can infer a difference in populations.
Inter-Quartile Range

11. Inter-Quartile Range Shift Overlap
Is one IQR shifted further up/down the scale than the other?
Overlap
Is there any overlap of IQR’s?
Quantify the overlap
Inter-Quartile Range

12. Overall Visible Spread
Overall Visible Spread is a VISUAL tool designed to help make decisions:
Estimate the OVS
You should sketch the OVS and cut it into sections depending on the size of the sample.
If sample ≈ 30 then estimate thirds
If sample ≈ 100 then estimate fifths
If sample ≈ 1000 then estimate tenths.
This can then be compared to the distance between the medians (DBM).
Overall Visible Spread

13. DBM vs OVS Estimate the DMB just as you estimate the OVS.
Sketch the distance between medians.
Compare the DBM to the OVS visually- this is not a calculation. The calculation should only ever be used in extremely close situations.
Make the call based on:
If sample size ≈ 30 then DBM > 1/3
If sample size ≈ 100 then DMB > 1/5
If sample size ≈ 1000 then DBM > 1/10
DBM vs OVS

14. IQR??

15. IQR?

16. IQR?