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What is an average? An average is a measure of the "middle" value of a set of data.Mode, Mean, and Median, are all types of averages.They can be used to help summarise a group of data.
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WALT……understand what the Mode isand how to identify it in data.
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Definition of Mode• The “mode” for a set of data is the number (or item) that occurs most frequently.• Sometimes data can have more than one mode. This happens when two or more numbers (or items)occur an equal number of times in the data. • A data set with two modes is called bimodal. • A data set with 3 modes is called Trimodal• It is also possible to have a set of data with no mode.
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How to find the Mode. Mode is the most common number Put the numbers in order Choose the number that appears the most frequently.Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6Put in order: 1, 2, 3, 3, 4, 5, 5, 5, 6, 6The class modal shoe size is 5.
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Find the mode in this data setClass high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.10, 1.20, .95, 1.25, 1.30, .75, .80, .90,.75, .80, .85, .90, .95,.95, 1.05,1.05, 1.05, 1.10, 1.10, 1.20, 1.25, 1.30 The mode is 1.05m
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Bimodal and trimodal BimodalData Set = 2, 5, 2, 3, 5, 4, 72, 2, 3, 4, 5, 5, 7Modes = 2 and 5 TrimodalData Set = 2, 5, 2, 7, 5, 4, 72, 2, 4, 5, 5, 7, 7Modes = 2, 5, and 7
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ExampleData Set= 3, 5, 6, 4, 7, 8, 9, 2, 1, 0What is the mode?0,1,2,3,4,5,6,7,8,9Is the mode = 0?Mode = no mode
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When might the Mode be used? The mode can be useful for dealing with categorical data. For example, if a sandwich shop sells 10 different types of sandwiches, the mode would represent the most popular sandwich. The mode can be useful for summarising survey data. The mode can be useful for election votes.
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Averages What other ways can we calculate the average of a set of data? We can use the Mean to give us an average of numerical data.
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WALT…understand what the Mean is and how to identify it in data.
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Definition of the Mean The „Mean‟ is the „Average‟ value of numerical data. The Mean (or average) is found by adding all scores together and dividing by the number of scores.
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Example Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6 Add up the numbers: 3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40 Divide by how many numbers: 40 ÷ 10 = 4 The class mean shoe size is 4
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Find the Mean Class high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.10, 1.20, .95, 1.2 5, 1.30, .75, .80, .90, 1.05 + 1.10 + 1.05 +.95 + .85 +1.05 + 1.10 + 1.20 + .95 + 1.25 + 1.30 + .75 + .80 + .90 = 14.3mMean = 14.3 divided by the number of people that jumped (14) 14.3 ÷ 14 = 1.02m
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Population of NZ Cities1600000140000012000001000000 800000 600000 400000 Population 200000 0 What is the mode? What is the mean?
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Work it out Mode = most common – 390,000 is the mode of the population of the NZ Cities on the graph. Mean = the average population of the NZ cities on the graph –200,000 + 60,000 + 390,000 + 390,000 + 125,000+ 1355,000 = 2520,000Mean = 2520,000 ÷ 6 = 420,000
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When to use the mean… The mean can give a good average value when the data is fairly evenly distributed as in the high jump heights. Class high jump heights (in metres) 1.05 + 1.10 + 1.05 +.95 + .85 +1.05 + 1.10 + 1.20 + .95 + 1.25 + 1.30 + .75 + .80 + .90 = 14.3mMean = 14.3 divided by the number of people that jumped (14) 14.3 ÷ 14 = 1.02m
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However It is not always suitable to use the mean to get an average of data when there is a huge variation in data.
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Example Population of NZ Cities1600000140000012000001000000 800000 600000 400000 Population 200000 0
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What is an average? , . An average is a measure of the "middle" value of a set of data.Mode, Mean, and Median, are all types of averages.They can be used to help summarise a group of data.
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RecapDefinition of Mode –The “Mode” for a set of data is thenumber (or item) that occurs mostfrequently.Definition of Mean –The “Mean” is the „Average‟ value ofnumerical data.
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Example. Class high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.05,1. 20, .95, .50, .80, .65, 1.05, 1.10,.95.95, 1.25, 1.30, .75, .80, .90, 1.00, 1.1 0, 1.15, 1.25, 1.10, 1.10, 1.15 What is the mode? What is the mean?
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WALT…..understand what the Median is and how to identify it in data.
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Definition of Median The Median is the middle value when numbers are put in order. To find the Median, place the numbers in numerical order and find the middle number. If the total number of values in the sample is even, the median is calculated by finding the mean of the two values in the middle.
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Find the mode How many children in your family?121086 Quantity420 Two Three Four Five Six
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Find the Mean .. How many children in your family?1210 8 6 Quantity 4 2 0 Two Three Four Five Six
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To find the mean…(10 x 2) + (10 x 3) + (5 x 4) + (3 x 5)+ (1 x 6) = 9191 ÷ 29 = 3.13 rounded to 3Mean = 3
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Find the. median . How many children in your family?1210 8 6 Quantity 4 2 0 Two Three Four Five Six
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To find the median… Put the numbers in order…2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6.The Median = 3
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Range Range is the gap from the biggest to smallest value. Put the numbers in order Take the smallest number away from the largest.Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6Put in order: 1, 2, 3, 3, 4, 5, 5, 5, 6, 6Subtract smallest from largest: 6 – 1 = 5Range: 5
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When should you use the Mean, Mode, or Median? Use the mean for data which is fairly evenly distributed. Use the median for data which has extreme differences in scores. Use the mode in categorical data where the original scores are known.
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