1. Stem and Leaf Diagrams Teach GCSE Maths

2. "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" © Christine Crisp Stem and Leaf Diagrams

3. Key: 3 5 means 35 hours Hours worked in 1 week by 30 men 21 28 300112222333444 355555566 4112 456 51 A stem and leaf diagram is used to display small data sets where the data are not grouped. e.g. The diagram below gives the number of hours worked in a particular week by a sample of 30 men. stem leaves tells us that the stem gives tens and the leaves give units. 35 is 3 tens and 5 units, so the key...

4. Decide with your partner how many hours are shown here. Ans: 46 ( the stem gives 40 and the leaf 6 ) The numbers on a stem and leaf diagram are always in order and increase away from the stem.

5. Key: 3 5 means 35 hours Hours worked in 1 week by 30 men 113 Ans: 2 How many men worked 31 hours during the week? What is the mode of the hours worked? 21 28 002222333444 355555566 4112 456 51 Ans: Mode is most, so mode = 35

6. Key: 6 2 means 62 mm Rainfall data 10 9 8 7 31 7 7 6 56 0 2 50 7 Remind your partner how to find the median of a data set. Can you find the median here? e.gThe diagram shows the average rainfall (mm) for Newton Rigg ( UK ) from 1971 – 2000 for Jan. to Nov. 3 Ans: Median rainfall is 73 mm The numbers are in order and there are 11 of them, so the median is the 6 th. 123 4 56 Tip: Check there are the same number of numbers before and after the median. (Here there are 5 before and 5 after) Adapted from Crown copyright data supplied by the Met Office

7. Suppose I now add December’s rainfall ( 109 mm ) to the rainfall data. Key: 6 2 means 62 mm Rainfall data 10 9 8 7 31 7 77 6 56 30 2 50 9 109 mm Tell your partner what the frequency is now. Ans: 12 The median is the average of the 6 th and 7 th values ! Median annual rainfall for Newton Rigg = ½( 73 + 77 ) = 75 mm Decide with your partner what the median is.

8.  Stem and Leaf diagrams are used for small, raw data sets (not grouped data). continued SUMMARY  The key gives the size of the numbers in the stem and the leaves. The stem here gives tens and the leaves give units. e.g. Key: 6 2 means 62 mm Rainfall data 10 9 8 7 31 7 77 6 56 30 2 50 9

9.  The median is found by counting out from the stem. If the frequency is an even number, we have to find the average of 2 numbers. There are always the same number of numbers before and after the median. Key: 6 2 means 62 mm Rainfall data: 11 months 10 9 8 7 31 7 77 6 56 0 2 50 3 Median = 73 mm Key: 6 2 means 62 mm 10 9 8 7 31 7 77 6 56 30 2 50 9 Rainfall data: 12 months Median = 75 mm

10. (a) Find the median time taken. (b) Find the range. (c) Find the mode. Exercise 1. The stem and leaf diagram shows the time taken for 15 students to walk to school. 05778 10025668 2555 38 Key: 1 6 represents 16 mins

11. (a) Exercise 1. The stem and leaf diagram shows the time taken for 15 students to walk to school. The median is 15 mins. 05778 10025668 2555 38 Key: 1 6 represents 16 mins Solution: 1234 5 67

12. (a) Exercise 1. The stem and leaf diagram shows the time taken for 15 students to walk to school. The median is 15 mins. (b)The mode is 25 mins. 05778 10025668 2555 38 Key: 1 6 represents 16 mins Solution:

13. (a) Exercise 1. The stem and leaf diagram shows the time taken for 15 students to walk to school. The median is 15 mins. (b)The mode is 25 mins. (c)The range is ( 38 – 5 ) = 33 mins. 05778 10025668 2555 38 Key: 1 6 represents 16 mins Solution:

14. Exercise January Max Temperatures for Sheffield 1985 to 2005 Key: 8 1 represents 8·1  C 347 4 50234 6459 712248 812459 90 2. (a)What was the lowest temperature ? (b)Find the median temperature. Adapted from Crown copyright data supplied by the Met Office

15. Exercise January Max Temperatures for Sheffield 1985 to 2005 Key: 8 1 represents 8·1  C 347 4 50234 6459 712248 812459 90 (b) (a)The lowest temperature is 3·4  C Solution: 12 34 5 6 789 There are 20 temperatures so the median is the average of the 10 th and 11 th.

16. Exercise January Max Temperatures for Sheffield 1985 to 2005 Key: 8 1 represents 8·1  C 347 4 50234 6459 712248 812459 90 (b) The median = 7·15  C (a)The lowest temperature is 3·4  C Solution: