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Measuresofcentraltendency 121117004155-phpapp01

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Jouaine Ombay
Jouaine Ombay

Central tendency refers to measures that characterize the middle or center of a data set. The three most common measures of central tendency are the mean, median, and mode. The mean is the average value found by dividing the sum of all values by the number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value in the data set. These measures help analyze and describe data in a simplified and representative way.

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Measuresofcentraltendency 121117004155-phpapp01
Measuresofcentraltendency 121117004155-phpapp01
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
Importance of the Measures of Central Tendency • • • • To find representative value To condense data To make comparisons Helpful in further statistical analysis
MEAN
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
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.
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
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:
Note: In 32 34 35 Mdn = 5th value Mdn = 36 Mdn = 35 36 37 38 39 47
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.
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.
Measuresofcentraltendency 121117004155-phpapp01
Measuresofcentraltendency 121117004155-phpapp01
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.
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.
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.
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.

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Measuresofcentraltendency 121117004155-phpapp01

  • 3. 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
  • 4. Importance of the Measures of Central Tendency • • • • To find representative value To condense data To make comparisons Helpful in further statistical analysis
  • 6. 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
  • 7. 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.
  • 8. 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
  • 9. 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:
  • 10. Note: In 32 34 35 Mdn = 5th value Mdn = 36 Mdn = 35 36 37 38 39 47
  • 11. 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.
  • 12. 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.
  • 15. 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.
  • 16. 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.
  • 17. 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.
  • 18. 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.