Organising data & statistical charts

Skills and methods in this topic, easy to hard

1. 1Kinds of dataCounted is discrete, measured is continuous

   MethodNumber of people: discrete; height: continuous; colour: qualitative

   Another way: A value in between?150.5 lies between 150 and 151: continuous

2. 2Frequency tablesThe frequencies add up to the number of data

   Method0 × 3 + 1 × 5 + 2 × 4 = 13 books

   Another way: Count each valueCount the 2s: 4 of them

3. 3Class limits, boundaries and marksA boundary is halfway between classes; mark = (lower + upper limit) ÷ 2

   Method40–49: boundaries 39.5 and 49.5, mark 44.5, width 10

   Another way: From the boundaries(39.5 + 49.5) ÷ 2 = 44.5; 49.5 − 39.5 = 10

4. 4Grouped frequency tablesClasses neither overlap nor leave gaps; frequencies add to the total

   Method60 or more: 5 + 4 + 1 = 10 people

   Another way: Count class by classCount all the values in the 40s: 3

5. 5Stem-and-leaf diagramsOne leaf, one value; the leaves run in order

   Method4 | 2 5 7 is 42, 45, 47

   Another way: Write the values out5 | 0 3 → 50, 53

6. 6HistogramsBar height = frequency; no gaps between bars

   MethodThe bar from 39.5 to 49.5 is the class 40–49

   Another way: Copy it into a table40–49: 3; 50–59: 7; 60–69: 5

7. 7Drawing stem-and-leaf diagrams and histogramsKeep empty stems; bars run boundary to boundary

   MethodData 41, 43, 62: stems 4, 5, 6, stem 5's row empty

   Another way: Sort the data first41, 43, 62 → 4 | 1 3, 6 | 2

8. 8What the diagrams tell usA histogram doesn't show the values inside a class

   Method5 in 60–69, 3 in 70–79: at least 3 scored 65 or more, at most 8

   Another way: Find a counter-exampleThe 5 might all score 60: so only 'at least 3'

9. 9Back-to-back stem-and-leaf diagramsThe left side too reads stem, then leaf

   MethodOn the left, 3 | 6 is 63, not 36

   Another way: Write two listsA: 52, 58, 63; B: 49, 61, 70

10. 10Compound bar chartsRead the key, then compare month by month

    MethodMarch: A 40, B 25, a difference of 40 − 25 = 15

    Another way: Copy it into a tableA: 40, 35, 50; B: 25, 45, 30

Worked examples

From different skills in this topic. Have a go first, then open each one for the answer and the working.

1. Example 1Kinds of data →

   Weights are measured to the nearest kg. A weight recorded as 61 kg is really at least kg.

   ▶Show the answer and working

   Answer: 60.5

   Weight is continuous, rounded to the nearest kg before it is recorded, so it may really be up to 0.5 kg less: 61 − 0.5 = 60.5.

2. Example 2Histograms →

   The histogram shows a team's scores. How many scored 50–59?

   ▶Show the answer and working

   Answer: 7

   Read across from the top of the 50–59 bar to the scale: 7.

3. Example 3Compound bar charts →

   The compound bar chart shows a club's new members in four months (male and female). How many new female members joined in the four months?

   ▶Show the answer and working

   Answer: 850

   Female is the second bar; add the four months from March: 350 + 100 + 50 + 350 = 850.