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US12332

US12332. Demonstrate knowledge of measures and displays used to compare data sets. Composite bar charts. Displays bivariate data (data with two variables) so it can be compared.

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US12332

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  1. US12332 Demonstrate knowledge of measures and displays used to compare data sets

  2. Composite bar charts Displays bivariate data (data with two variables) so it can be compared e.g. Draw a composite bar chart for this set of data, which gives information about the amount of elements (g) in 1 kg of three different types of fats. Element content in fat 42 34 46 68 54 72 Mass of element (g) Total columns to work out height of axis/bars Elements go on bottom axis Draw bars for saturated fats Bars for polyunsaturated fats is placed on top etc Add a key Aluminium Carbon Iron Saturated fat Polyunsaturated fat Monounsaturated fat

  3. Averages 1. Mean - easy to calculate but is affected by extreme values - to calculate use: Sum of all values Total number of values Push equals on calculator BEFORE dividing e.g. Calculate the mean of 6, 11, 3, 14, 8 6 + 11 + 3 + 14 + 8 42 Mean = = = 8.4 5 5

  4. Stem and Leaf Plots – records and organises data – most significant figures form the stem and the final digits the leaves – can be in back to back form in order to compare two sets of data e.g. Place the following heights (in m) onto a back to back stem and leaf plot BOYS = 1. 59, 1.69, 1.47, 1.43, 1.82, 1.70, 1.73, 1.35, 1.76, 1.68, 1.62, 1.84, 1.45, 1.50, 1.54, 1.73, 1.84, 1.71, 1.66 GIRLS = 1. 44, 1.46, 1.63, 1.29, 1.48, 1.57, 1.51, 1.42, 1.34, 1.45, 1.57, 1.59, 1.42 Unordered Graph of Heights Ordered Graph of Heights Boys Girls Boys Girls   1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 4 ,4 ,2 4, 4, 2 1 ,3 ,6 ,3 ,0 6, 3, 3, 1, 0 6 ,2 ,8 ,9 3 9, 8, 6, 2 3 4 ,0 ,9 7, 1, 7, 9 9, 4, 0 1, 7, 7, 9 5 ,3 ,7 4, 6, 8, 2, 5, 2 7, 5, 3 2, 2, 4, 5, 6, 8 5 4 5 4 9 9 Place the final digits of the data on the graph on the correct side

  5. Calculating Statistics from Stem and Leaf Plots Graph of Heights Boys Girls   1.8 1.7 1.6 1.5 1.4 1.3 1.2 To find placement of median and LQ/UQ use: n + 1 2 For each statistic, make sure to write down the whole number, not just the ‘leaf’! 4, 4, 2 6, 3, 3, 1, 0 9, 8, 6, 2 3 9, 4, 0 1, 7, 7, 9 When finding median, LQ and UQ, make sure you count/cross in the right direction! 7, 5, 3 2, 2, 4, 5, 6, 8 5 4 9 e.g. From the ordered plot state the minimum, maximum, LQ, median, UQ, IQR and range statistics for each side BOYS GIRLS Median = 13 + 1 = 7 2 Minimum: 1.35 m 1.29 m Maximum: 1.84 m 1.63 m LQ: 1.50 m 1.42 m LQ/UQ = 6 + 1 = 3.5 2 Median: 1.68 m 1.46 m UQ: 1.73 m 1.57 m IQR: 1.73 – 1.50 = 0.23 m 1.57 – 1.42 = 0.15 m Range: 1.84 – 1.35 = 0.49 m 1.63 – 1.29 = 0.34 m Remember: If you find it hard to calculate stats off graph, write out data in a line first!

  6. Note: Use the minimum and maximum values to determine length of scale Box and Whisker Plots – shows the minimum, maximum, LQ, median and UQ – ideal for comparing two sets of data e.g. Using the height data from the Stem and Leaf diagrams, draw two box and whisker plots (Boys and Girls) Box and Whisker Plots of Boys and Girls Heights Males Minimum LQ Median UQ Maximum Females Question: What is the comparison between the boy and girl heights? ANSWER? EVIDENCE?

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