Stem and leaf diagrams Sometimes called ‘stem and leaves’ too

They really are as simple as they seem

Simply a way of showing the values of data

Example…….. Here are the weights of some aardvarks (kg): 12, 28, 17, 17, 19, 23, 9, 7, 25, 34, 21 Stem and leaf might look like this: Weight of aardvarks 0 9, 7 12, 7, 7, 9, 28, 3, 5, 1 KEY is 12kg STEMLEAF OR LEAVES Don’t need to write this usually

Your ‘stem and leaf’ must have a… 1.Title 2.Key – so that other people can work out what your values are.

An ordered ‘stem and leaf’…. Has the values in size order.

So for our example before… Weight of aardvarks 0 9, 7 12, 7, 7, 9, 28, 3, 5, 1 KEY is 12kg The ordered ‘stem and leaf’ would be: Weight of aardvarks 0 7, 9 12, 7, 7, 9, 21, 3, 5, 8 KEY is 12kg What weight does the ‘5’ represent?

Show the following data as a stem and leaf diagram I.Q. scores of Year 10 girls: 105, 98, 112, 94, 130, 121, 98, 104, 100, 108, 112, 104, 101, 97, 104 I.Q. scores of Year 10 girls 9 8, 4, 8, , 4, 0, 8, 4, 1, , KEY 11 2 means 112

Now ‘order it’ I.Q. scores of Year 10 girls (unordered) 9 8, 4, 8, , 4, 0, 8, 4, 1, , KEY 11 2 means 112 I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, , 1, 4, 4, 4, 5, , KEY 11 2 means 112

The ordered one can be used to find lots of information

Mode…. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, , 1, 4, 4, 4, 5, , KEY 11 2 means 112 Mode – most common In this case 104

Range …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, , 1, 4, 4, 4, 5, , KEY 11 2 means 112 Highest value – lowest value In this case: Range = 130 – 94 = 36

Median …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, , 1, 4, 4, 4, 5, , KEY 11 2 means Put in size order (already done); 2.then find the middle value In this case we have 15 values so we want the median = th value along

Lower Quartile …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, , 1, 4, 4, 4, 5, , KEY 11 2 means Put in size order (already done); 2.then find the value a quarter of the way up In this case we have 15 values so we want the Lower quartile = 98 4 th value along

Upper Quartile …. I.Q. scores of Year 10 girls (ordered) 9 4, 7, 8, , 1, 4, 4, 4, 5, , KEY 11 2 means Put in size order (already done); 2.then find the value three- quarters of the way up In this case we have 15 values so we want the Upper quartile = th value along

You now know enough to be able to draw a ‘box and whisker diagram’ Smallest value Largest value median Lower quartile upper quartile I.Q. Score

Now for the boys……..

Show the following data as a stem and leaf diagram I.Q. scores of Year 10 boys: 103, 98, 112, 99, 108, 122, 98, 104, 100, 108, 112, 104, 101, 97, 104, 108, 99, 108, 102 I.Q. scores of Year 10 boys 9 8, 9, 8, 7, ,8,4,0,8,4,1,4,8,8,2 11 2, KEY 11 2 means 112

Now ‘order it’ I.Q. scores of Year 10 boys (unordered) 9 8, 9, 8, 7, ,8,4,0,8,4,1,4,8,8,2 11 2, KEY 11 2 means 112 I.Q. scores of Year 10 boys (ordered) 9 7, 8, 8, 9, ,1,2,3,4,4,4,8,8,8,8 11 2, KEY 11 2 means 112

Mode …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, ,1,2,3,4,4,4,8,8,8,8 11 2, KEY 11 2 means 112 Mode – most common In this case 108

Range …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, ,1,2,3,4,4,4,8,8,8,8 11 2, KEY 11 2 means 112 Highest value – lowest value In this case: Range = 122 – 97 = 25

Median …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, ,1,2,3,4,4,4,8,8,8,8 11 2, KEY 11 2 means Put in size order (already done); 2.then find the middle value In this case we have 19 values so we want the median = th value

Lower Quartile …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, ,1,2,3,4,4,4,8,8,8,8 11 2, KEY 11 2 means Put in size order (already done); 2.then find the value a quarter of the way up In this case we have 19 values so we want the Lower quartile = 99 5 th value

Upper Quartile …… I.Q. scores of Year 10 boys 9 7, 8, 8, 9, ,1,2,3,4,4,4,8,8,8,8 11 2, KEY 11 2 means Put in size order (already done); 2.then find the value three- quarters of the way up In this case we have 19 values so we want the Upper quartile = th value

Now draw a box and whisker diagram to compare the I.Q. of boys and girls you can draw this one on the same diagram as before.

Here we go … I.Q. Score GIRLS BOYS What can you say about boys and girls I.Q.s ?