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Statistics: Mean, Median, Mode & Range

Statistics: Mean, Median, Mode & Range. Measures of Central Tendency. Mean - The sum of the data divided by the number of items in the data set. - Most useful when the data has no extreme values

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Statistics: Mean, Median, Mode & Range

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  1. Statistics: Mean, Median, Mode & Range

  2. Measures of Central Tendency Mean - The sum of the data divided by the number of items in the data set. - Most useful when the data has no extreme values Example: Find the mean of the following data: 65, 79, 85, 92, 68, 82, 77, 90, 97, 60, 80, 87, 75, 82, 79, 93. -Add the scores together: 65+79+85+92+68+82+77+90+97+60+80+87+75+82+79+93 =1291 -Divide the sum by the number of items in the set: 1291 ÷ 16 = 80.6875 -The mean of the data is 80.7.

  3. Measures of Central Tendency Median – the middle number of the data ordered from least to greatest, or the mean of the middle two numbers. - Most useful when the data has no extreme values and there are no big gaps in the middle of the data. Example: Find the median of the following data: 65, 79, 85, 92, 68, 82, 77, 90, 97, 60, 80, 87, 75, 82, 79, 93. Put the data in order from the least to the greatest: 60, 65, 68, 75, 77, 79, 79, 80, 82, 82, 85, 87, 90, 92, 93, 97 Find the middle number. If there are two middle numbers, find the mean of those two numbers. 80+82 = 162 162 ÷ 2 = 81 Cross out the numbers from each end to find the middle. The median of the data is 81.

  4. Measures of Central Tendency Mode – The number or numbers that occur most often. • Most useful when the data has many identical numbers. Example: Find the mode of the following data: 65, 79, 85, 92, 68, 82, 77, 90, 97, 60, 80, 87, 75, 82, 79, 93. Look for numbers that occur more than once. There are two modes to this data set. They are 79 and 82. *If there aren’t any numbers that occur more than once, the mode is none (not zero).

  5. Measures of Variation • Range • Indicates how spread out the data are. • The difference between the largest number in the data set and the smallest number in the data set. Example: Find the range of the following data: 65, 79, 85, 92, 68, 82, 77, 90, 97, 60, 80, 87, 75, 82, 79, 93. Highest score - lowest score 97 - 60 The range for the data set is 37.

  6. Practice Problems • Find the mean, median and mode of the following data set: 81, 78, 97, 78, 78, 77, 59, 87, 78, 97, 47, and 94. Mean 873÷11=79.3636… Mean = 79 Median: 47, 59, 77, 78, 78, 78, 81, 87, 94, 97, 97 Median is 78 Mode: 78 Range: 97 – 47 = 50

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