1. 1 MEASURES OF CENTRAL TENDENCY AND DISPERSION AROUND THE MEDIAN

2. 2 M EASURES OF CENTRAL TENDENCY A Measure of Central Tendency is a single value representing a set of data Three Measures of Central Tendency are – –Mean (dealt with first in Grade 7) – –Median (dealt with first in Grade 6) – –Mode (dealt with first in Grade 5)

3. 3 Mean, Median and Mode The mean – the equal shares average; The median – the middle value; The mode – the value that occurs most often. Their use depends on the sort of information you need your data to show.

4. 4 Activity 1 1) 1) 50,4% 2) 2) 3) 3) Maths - 57%, 4) 4) 63% - English & Geography Test no. HistBiolTech Math EngGeogZulu Mark25%31%37% 57%63% 77%

5. 5 Organising Data Using a Stem-And-Leaf Diagram 32 ; 56 ; stemleaves 32 4 56 6 7 The first number is 32: The stem is 3 and the leaf is 2 The second number is 56: The stem is 5 and the leaf is 6

6. 6 The leaf is the ‘units’ digit – i.e. furthest to the right in the number. The stem is the ‘tens’ digit – i.e. furthest to the left in the number. If the number includes ‘hundreds’ and ‘thousands’ digits then the stem includes these digits as well. If the list of numbers includes a single digit number then the stem must be 0.

7. 7 Redraw the display with the leaves written in ascending order. Leaves must be carefully written underneath each other. Squared paper! Find median (or middle value) by counting the leaves. Two data sets can be written as displays on either side of the same stem.

8. 8 Activity 2 StemLeaves 0233566678899 12222345588 20000245 30 KEY: 2/5=25 Median lies between 15 th and 16 th value. Median is 12 hrs Mode = 20 hrs and 12 hrs We say the data is bimodal

9. 9 Range Range = highest value – lowest value 200 cm 150 cm 100 cm

10. 10 Quartiles Quartiles divide the distribution into four equal parts. Set of data items divided into 4 equal parts: Lower quartileMedianUpper quartile (Q 1 ) (M)(Q 3 )

11. 11 The lower quartile (Q 1 ) is a quarter of the way through the distribution, The middle quartile which is the same as the median (M) is midway through the distribution. The upper quartile (Q 3 ) is three quarters of the way through the distribution.

12. 12 Finding quartiles on Stem-and-Leaf Example: Eighteen numbers were listed on a stem and leaf plot as follows (n = 18) StemLeaves 11 2 20 5 30 0 0 2 5|9 40 0 0 2 5 8 50 6 70 KEY: 3/5=35 Median lies between 9 th and 10 th data item. Q 1 lies in 5 th position. Q 3 lies in the 14 th position.

13. 13 Activity 3 1. a) M=7Q 1 =5Q 3 =9 b) M=28,5Q 1 =22Q 3 =35 c) M=16,5Q 1 =13Q 3 =19

14. 14 Leaves for Set 1StemLeaves for set 2 19 27 378 98540289 7752211509 7643068 327369 0857 905 KEY: 8/0=80 Set 1:Set 2: M = 57M = 54,5 Q 1 = 51Q 1 = 40 Q 3 = 66Q 3 = 79

15. 15 Five-Number Summaries The five-number summary for a set of data values consists of The Minimum value The Lower quartile (Q1) The Median (M) The Upper quartile (Q3) The Maximum value

16. 16 Activity 4 Min = 1 year Q 1 = 8 years M = 12 years Q 3 = 15 years Maximum = 41 years

17. 17 Box and Whisker Diagrams It is a diagram of the five-number summary. For example, consider the following data: 1,5,7,8,8,14,17. Median = 8 Q 1 = 5 Q 3 = 14 Minimum = 1 Maximum = 17

18. 18 The box shows the middle 50% or half of the data. There is the same number of data items in each of the four groups. The varying lengths are influenced by the value of the data items

19. 19 The Interquartile Range The IQR shows the spread of the middle section of data. The IQR shows the spread of the middle section of data. IQR = Q 3 – Q 1 IQR = Q 3 – Q 1 Semi-interquartile range = IQR ÷ 2 Semi-interquartile range = IQR ÷ 2