1. SHS Maths | shsmaths.wordpress.com Year 9 – Data Handling

2. Measures of Average There are three different measures of average:  Mode – the most common number  Median – the middle number when the data is in order  Mean – the number you get when you add up your data and share it equally between. Eg: Numbers of Easter Eggs eaten by 10 people: 3, 5, 1, 0, 7, 4, 2, 3, 5, 3 Mode = Median = Mean =

3. Measures of Spread At the moment, you’ve probably only met one measure of spread – the range. Range = Highest data value – lowest Eg for our Easter Egg data: 3, 5, 1, 0, 7, 4, 2, 3, 5, 3 Range =

4. Frequency Tables Imagine instead of asking 10 people about how many Easter Eggs, we asked 100. Writing this data in a list would be LONG. So we use a table instead: Number of EggsFrequency 013 126 233 320 48

5. Mode / Median using Table ‘Modal Value’ is the most common: Median Value is half way up: Number of EggsFrequency 013 126 233 320 48

6. Mean Using Table To find the mean, we multiply the number of eggs by the frequency for each group. Then add up this column and divide by the total frequency. Number of EggsFrequency 013 126 233 320 48 Eggs x f 0 x 13 = 0 1 x 26 = 26 2 x 33 = 66 3 x 20 = 60 4 x 8 = 32 Total = 184Total = 100 Mean = 184 / 100 = 1.84 Eggs

7. Questions 1 – Do Question 2 of Rev. Ex 1.7 on p. 29 2 – Find the mode, median and mean for this set of data on nesting birds eggs: Number of Eggs in nest Number of nests 34 410 52 62 71

8. Mean of Grouped Frequency Diameter (mm) Freq 28 ≤ d < 302 30 ≤ d < 326 32 ≤ d < 367 36 ≤ d < 405 Totals: Because the data is in groups, we can’t just multiply. Instead, we assume that all the measurements are in the middle of each group Mid Point 29 31 34 Mid Point x freq 29 x 2 = 58 31 x 6 = 186 34 x 7= 238 Now fill in the totals… Mean is total divided by freq =

9. Practice Questions Page 245, Qu 1 a, c and 2 a - c

10. Frequency Polygons – Discrete Data Example – Frequency Polygon for survey of 136 families. We simply plot each frequency, and then join with a straight line.

11. Frequency Polygon – Grouped Data Eg: Weights of 100 parcels. We plot each point in the middle of the group. We can plot more than one polygon on the same axes. Data for sample of another 100 parcels.

12. Practice Questions Page 250. Qu 1, 3

13. Moving Averages Some sorts of data go in cycles.  Temperatures over a day  Sales of shoes over days of the week  Sales over a year For cyclical data like this we have to use a moving average to iron out the variation.

14. Year199619971998 Quarter123412341234 Sales 189244365262190266359250201259401265 265.25 270.75 269.25 4 Period Moving Average

15. Year199619971998 Quarter123412341234 Sales 189244365262190266359250201259401265 4 period Moving Average Quarters1-42-53-64-75-86-97-108-119-12 Moving Average 265265.25270.75269.25266.25269267.25277.75281.5

16. Year199619971998 Quarter123412341234 Sales 189244365262190266359250201259401265 1 23 4 1 23 4 1 23 4 100 200 300 400 500 x 1996 1997 1998 x x x x x x x x x x x Quarters1-42-53-64-75-86-97-108-119-12 Moving Average 265265.25270.75269.25266.25269267.25277.75281.5 x xx x xx x x x