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

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 =

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 =

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

Mode / Median using Table ‘Modal Value’ is the most common: Median Value is half way up: Number of EggsFrequency

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 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

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

Mean of Grouped Frequency Diameter (mm) Freq 28 ≤ d < ≤ d < ≤ d < ≤ 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 Mid Point x freq 29 x 2 = x 6 = x 7= 238 Now fill in the totals… Mean is total divided by freq =

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

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

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.

Practice Questions Page 250. Qu 1, 3

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.

Year Quarter Sales Period Moving Average

Year Quarter Sales period Moving Average Quarters Moving Average

Year Quarter Sales x x x x x x x x x x x x Quarters Moving Average x xx x xx x x x