Measures of central tendencyPresentation Transcript
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 CentralTendency• To find representative value• To condense data• To make comparisons• Helpful in further statistical analysis
Example:The marks of seven students in a mathematics test with amaximum possible mark of 20 are given below: 15 13 18 16 14 17 12Find 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 thathad a maximum possible mark of 50 are givenbelow: 47 35 37 32 38 39 36 34 35Find the median (mdn) of this set of data values.
Solution:Arrange the data values in order from the lowestvalue to the highest value: 32 34 35 35 36 37 38 39 47The fifth data value, 36, is the middle value in thisarrangement..: mdn = 36Formula:
Note: If the list has an even number of entries, themedian is equal to the sum of the two middle (aftersorting) numbers divided by two.Example:The marks of eight students in a math test that had amaximum possible mark of 20 are given below: 12 18 16 21 10 13 17 19Find the median of this set of data values.
Solution: Arrange the data values in order from thelowest value to the highest value: 10 12 13 16 17 18 19 21The number of values in the data set is 8, whichis even. So, the median is the average of thetwo middle values.
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 48The mode is 48 since it occurs most often.
Example:The test scores of 9 seventh grade students arelisted below. Find the mode. 82, 92, 75 , 91, 92, 89, 95, 100, 86The 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.