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# Measuresofcentraltendency 121117004155-phpapp01

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• 1. What is Central Tendency? Measures of Central Tendency: - one type of summary statistic - are measures of location within a distribu-tion - A measure that tells us the middle of a bunch of data lies - 3 most common measures of central tendency are mean, median, mode
• 2. Importance of the Measures of Central Tendency • • • • To find representative value To condense data To make comparisons Helpful in further statistical analysis
• 3. MEAN
• 4. Example: The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: 15 13 18 16 14 17 12 Find the mean of this set of data values. Solution: 15
• 5. MEDIAN • The median (mdn) of a set of data values is the middle value of the data set when it has been arranged in ascending order. That is, from the smallest value to the highest value.
• 6. Note: • If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. Example: The marks of nine students in a geography test that had a maximum possible mark of 50 are given below: 47 35 37 32 38 39 36 34 Find the median (mdn) of this set of data values. 35
• 7. Solution: Arrange the data values in order from the lowest value to the highest value: 32 34 35 35 36 37 38 39 47 The fifth data value, 36, is the middle value in this arrangement. .: mdn = 36 Formula:
• 8. Note: In 32 34 35 Mdn = 5th value Mdn = 36 Mdn = 35 36 37 38 39 47
• 9. Note: If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. Example: The marks of eight students in a math test that had a maximum possible mark of 20 are given below: 12 18 16 21 10 13 17 19 Find the median of this set of data values.
• 10. Solution: Arrange the data values in order from the lowest value to the highest value: 10 12 13 16 17 18 19 21 The number of values in the data set is 8, which is even. So, the median is the average of the two middle values.
• 11. MODE • For lists, the mode is the most common (frequent) value. • A data set has no mode when all the numbers appear in the data with the same frequency. • A data set has multiple modes when two or more values appear with the same frequency.
• 12. Example: Find the mode of the following data set: 48 44 48 45 42 49 48 The mode is 48 since it occurs most often.
• 13. Example: The test scores of 9 seventh grade students are listed below. Find the mode. 82, 92, 75 , 91, 92, 89, 95, 100, 86 The mode is 92 since it occurs most often.
• 14. Note: • It is possible for a set of data values to have more than one mode. • If there are two data values that occur most frequently, we say that the set of data values is bimodal. • If there is no data value or data values that occur most frequently, we say that the set of data values has no mode.