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Mode, Median and Range Aim: To find the mode, median and range, and the modal class for grouped data.

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Put these numbers in numerical order with the smallest first. 7, 3, 9, 2, 10, 8, 5, 4, 14, 12 2,3,4,5,7,8,9,10,12,14, 34, 67, 38, 19, 44, 57, 24, 31, 62, 20 19, 20, 24, 31, 34, 38, 44, 57, 62, 67

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2, -3, 1, 4, -4, 0, 5, -2 -5 1-4-3-20245 -4-3-2 0 23451

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Averages An average is a useful statistic because it represents a whole set of values by just a single or typical value. Where have you heard the word average before? Where have you seen it used?

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The Mode The mode is a type of average The mode is the value that occurs most often in a set of data Example 5, 6, 8, 2, 4, 5, 3, 5 MODE = 5 Sometimes there is no mode because either all the values are different, or no single value occurs more often than other values

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What letter does your first name begin with? What is the mode first letter for a name in class 7Y2? THE MODE DOESN’T HAVE TO BE A NUMBER

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Mode, Median and Range Aim: To find the mode, median and range, and the modal class for grouped data. PAGE 52 EXERCISE 5A QUESTION 1 THE MODE

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The Median The median is another type of average The median is the middle value for a set of data when the values are put in numerical order. Example 6, 8, 3, 7, 5, 2, 4 in order2, 3, 4, 5, 6, 7, 8 Median = 5 For an odd number of values in data set, there is only one middle value. This is the median.

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What is the median test score for the following set of results? 5, 7, 7, 8, 10, 12, 14, 15 For an even number of values in a data set, there are two middle values. The median is the value in the middle of these two values. Median = 9

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The median PAGE 51 EXERCISE 5A QUESTION 2

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The Range The range is not an average. The range of a set of data is the largest value minus the smallest value. It shows how the data is spread out. A small range showsthat the values in a set of data are similar in size A large range showsthat the values differ considerably

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Find the range: What number month were you born in? Range = Largest number – smallest number Range = What does this tell us about the birthdays of class 7Y2? For example, January = 1, June = 6, and December = 12

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The Range PAGE 51 EXERCISE 5A QUESTION 3

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Modal Class For grouped data such as the example below, we cannot find the mode. Time (Mins.)Frequency 0-22 3-54 6-83 9-111 Instead, we find the MODAL CLASS. This is the group that occurs most often. Modal class = 3-5 Why isn’t it possible to calculate an exact mode or median from grouped data?

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Modal Class PAGE 52 EXERCISE 5A QUESTION 6

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Write down: 5 numbers with a mode of 7 7 numbers with a median of 3 7 numbers with a mode of 6 and a median of 12 7 numbers with a mode of 5, median of 8, and a range of 10

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Extension PAGE 51/52 EXERCISE 5A QUESTIONS 4, 5, AND 7

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Central Tendency Mean – the average value of a data set. Add all the items in a data set then divide by the number of items in the data set.

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