1 Further Maths Chapter 2 Summarising Numerical Data

2 Summary Statistics for Numerical Data The two most commonly used types of statistics are classified as: – Measures of centre – Measures of spread

3 The Median A measure of centre The median is the middle value when the data is ordered. The median depends on position in the set of data and so is not distorted by extreme values and outliers.

4 Range & Interquartile Range: Measures of Spread The value and the minimum value. The Interquartile Range (IQR) is the spread of the middle 50% of the data Range is the difference between the maximum.

5 Calculating the median Place numbers in ascending order Median = 3(5 th score)

6 Calculating the Range Min = 1 Max = 9 Range = Max – Min Range = 9 – 1 Range = 8

7 Calculating the Quartiles Lower Quartile (Q 1 ) Upper Quartile (Q 3 ) Q 1 = 1.5Q 3 = 8 Median (Q 2 ) =3 IQR = Q 3 – Q 1 IQR = 8 – 1.5 IQR = 6.5

8 Stem and Leaf Plots There are 22 scores The median will be between the 11 th and 12 th score. Lower Quartile = 23 Upper Quartile = 40 IQR = 40 –23 IQR = 17 Exercise 2A Pages 39 – 40 Questions 1-7

9 Five number summary median minimum maximum Lower Quartile Q 1 Upper Quartile Q IQR = 6.5

10 Five Number Summary Min = 1 Q 1 = 1.5 Median = 3 Q 3 = 8 Max = 9

11 Box and Whisker Plot A Box and Whisker Plot illustrates the 5 number summary. It is often used as a visual comparison of similar data sets. The statistics median, IQR and Range can be easily observed from a boxplot.

12 Box and Whisker Plot The box represents the middle 50% of the scores ie the IQR Each whisker represents 25% of the scores

13 Box and whisker plot Exercise 2B Page 44 Question 1 and 2

14 Box Plot with Outliers Outliers are identified using the limits Q 1 – 1.5*IQR and Q *IQR Any data values outside these boundaries are marked with an asterix on the boxplot.

15 Boxplot with outliers Min = Q 1 = Med = Q 3 = Max = IQR = Q *IQR = Q *IQR = – 1.5*14 = *14= will be an outlier Boxplot limits

16 Boxplot with outliers

17 Using a calculator Calculator display Exercise 2B Questions 3 – 6

18 Relating the shape of a histogram to a box plot Symmetric

19 Relating the shape of a histogram to a box plot

20 Relating the shape of a histogram to a box plot

21 Questions Exercise 2C Page 47 All

22 Comparing Boxplots

23 Questions Exercise 2D Page 49 All

24 That’s All, Folks!