1. Stem and Leaf Diagrams © Christine Crisp “Teach A Level Maths” Statistics 1

2. Stem and Leaf Diagrams "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" Statistics 1 AQA EDEXCEL MEI/OCR OCR

3. Stem and Leaf Diagrams You met some statistical diagrams when you did GCSE. The next three presentations and this one remind you of them and point out some details that you may not have met before. We will start with stem and leaf diagrams ( including back-to-back ). Stem and leaf diagrams are sometimes called stem plots.

4. Stem and Leaf Diagrams Weekly hours of 30 men 5 4 4 3 3 2 2 51 456 4112 355555566 300112222333444 28 21 e.g. The table below gives the number of hours worked in a particular week by a sample of 30 men 35413331304535365132 302835343335363242 33314121343534463235 The stem shows the tens... I’ll use intervals of 5 hours to draw the diagram i.e. 20-25, 26-30 etc. and the leaves the units e.g. 46 is 4 tens and 6 units

5. Stem and Leaf Diagrams Weekly hours of 30 men e.g. The table below gives the number of hours worked in a particular week by a sample of 30 men 51 456 4112 355555566 300112222333444 28 21 I’ll use intervals of 5 hours to draw the diagram i.e. 20-25, 26-30 etc. 35413331304535365132 302835343335363242 33314121343534463235 e.g. 46 is 4 tens and 6 units Weekly hours of 30 men The stem shows the tens... and the leaves the units

6. Stem and Leaf Diagrams Weekly hours of 30 men e.g. The table below gives the number of hours worked in a particular week by a sample of 30 men 51 456 4112 355555566 300112222333444 28 21 I’ll use intervals of 5 hours to draw the diagram i.e. 20-25, 26-30 etc. 35413331304535365132 302835343335363242 33314121343534463235 e.g. 46 is 4 tens and 6 units Weekly hours of 30 men N.B. 35 goes here... not in the line below. The stem shows the tens... and the leaves the units

7. Stem and Leaf Diagrams e.g. The table below gives the number of hours worked in a particular week by a sample of 30 men 51 456 4112 355555566 300112222333444 28 21 I’ll use intervals of 5 hours to draw the diagram i.e. 20-25, 26-30 etc. 35413331304535365132 302835343335363242 33314121343534463235 e.g. 46 is 4 tens and 6 units We must show a key. Key: 3 5 means 35 hours Weekly hours of 30 men The stem shows the tens... and the leaves the units

8. Stem and Leaf Diagrams 51 456 4112 355555566 300112222333444 28 21 Weekly hours of 30 men If you tip your head to the right and look at the diagram you can see it is just a bar chart with more detail. Points to notice: The leaves are in numerical order The diagram uses raw ( not grouped ) data Key: 3 5 means 35 hours

9. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. Median: The median is the middle item,... Tip: To find the middle use where n is the number of items of data. so with 30 observations we need the th item, the average of 15 and 16.

10. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. 15 th Median: The median is the middle item,... so with 30 observations we need the th item, the average of 15 and 16. Key: 3 5 means 35 hours

11. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. 15 th 16 th Median: The median is the middle item,... so with 30 observations we need the th item, the average of 15 and 16. Key: 3 5 means 35 hours

12. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. 15 th 16 th Since the 15 th and 16 th items are both 34, the median is 34. Median: The median is the middle item,... so with 30 observations we need the th item, the average of 15 and 16. ( If the values are not the same we average them. ) Key: 3 5 means 35 hours

13. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. For the lower quartile (LQ) we first need 7 th Key: 3 5 means 35 hours

14. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. 7 th 8 th For the lower quartile (LQ) we first need Key: 3 5 means 35 hours

15. Stem and Leaf Diagrams Finding the median and quartiles Finding these is easy because the data are in order. 7 th 8 th The lower quartile is 32. For the lower quartile (LQ) we first need Key: 3 5 means 35 hours

16. Stem and Leaf Diagrams Finding the median and quartiles If the values of the 7 t h and 8 th observation are not the same, we interpolate to find the LQ. and we want the 7·75 th value, we need to add 0·75 of the gap between the 7 th and 8 th to the 7 th value. e.g. If we had 7 th value: 32 8 th value: 36 So, The gap is 36 – 32 = 4. 0.75 of 4 is 3. LQ = 32 + 3 = 35

17. Stem and Leaf Diagrams Finding the median and quartiles For the upper quartile (UQ), we first need ( or from the top end ) Key: 3 5 means 35 hours

18. Stem and Leaf Diagrams Finding the median and quartiles 23 rd For the upper quartile (UQ), we first need ( or from the top end ) Key: 3 5 means 35 hours

19. Stem and Leaf Diagrams Finding the median and quartiles 23 rd 24 th For the upper quartile (UQ), we first need ( or from the top end ) Key: 3 5 means 35 hours

20. Stem and Leaf Diagrams Finding the median and quartiles 23 rd 24 th The upper quartile is 36. The interquartile range (IQR) = UQ  LQ = 36 – 32 = 4 For the upper quartile (UQ), we first need ( or from the top end ) Key: 3 5 means 35 hours

21. Stem and Leaf Diagrams 12 82 444333222211003 665555553 2114 654 15 Weekly hours of 30 men Key: 3 5 means 35 hours  Stem and Leaf diagrams are used for small, raw data sets (not grouped data). e.g.  The leaves are in numerical order ( away from the stem ) stem leaves  The diagram must have a title and a key. continued SUMMARY

22. Stem and Leaf Diagrams  The median is the th piece of data.  The quartiles are found at the th position and the th position. ( If necessary, average 2 data items )  The interquartile range (IQR) = UQ  LQ ( upper quartile – lower quartile )  If necessary, we can interpolate to find the LQ and UQ.

23. Back-to-Back Stem and Leaf Diagrams 43 0 88665555 444333222 8 3310 551 4421 Back-to-back stem and leaf diagrams can be used to compare 2 sets of data relating to the same subject. In our example we could add the data for 30 women. Women Notice how easily we can compare the variability of the 2 data sets Key: 5 3 means 35 hrs

24. Back-to-Back Stem and Leaf Diagrams 4 5 6 7 8 9 January Max Temperatures 1985 to 2005 Sheffield 116 25 31579 4003489 168 1258 2 Braemar 74 54320 954 84221 95421 0 Exercise Find the medians and quartiles. What can you say about the temperatures of the 2 places? Key: 3 4 means 3·4  C Key: 3 4 means 4·3  C

25. Back-to-Back Stem and Leaf Diagrams Answer: The places have similar variability in temperature but Sheffield is about 2 ·7  C warmer than Braemar. MedianLQUQ Braemar 4·44·43·63·65·95 Sheffield 7·17·15·358·15

27. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

28. Stem and Leaf Diagrams Weekly hours of 30 men 2 2 3 3 4 4 5 12 82 444333222211003 665555553 2114 654 15 Key: 3 5 means 35 hours  This is used for small, raw data sets (not grouped data). e.g.  The leaves are in numerical order ( away from the stem ) stem leaves  The diagram must have a title and a key. SUMMARY

29. Stem and Leaf Diagrams  The median is the th piece of data.  The quartiles are found at the th position and the th position. ( If necessary, average 2 data items )  If necessary, we can interpolate to find the LQ and UQ.  The interquartile range (IQR) = UQ  LQ ( upper quartile – lower quartile )

30. Stem and Leaf Diagrams