Measures Of Central Tendency

“AVERAGES”

Measures Of Central Tendency• In finding the single number that you felt best described the position at

which you grabbed the ruler, you found your typical or average performance.

• Measures of central tendency are measures that allow you to describe a typical value in a data set. They include the mean, median, and mode.

Measures Of Central TendencyMEAN 4, 5, 7, 16, 23 The mean is the average of all numbers in a set of data. Because the median and mode are often called averages as well, it is called the mean.

To find the mean, add all of the numbers in the data set and then divide that sum by how many numbers were added together to get that sum.Ex, 4, 5, 7, 16, 23 (4 + 5 + 7 + 16 + 23 = 55) 55/5 = 11 The mean is 11

(There are 5 numbers that were added together to get 55, so therefore 55/5 = 11.)

Advantage: Information is given about the sum of the values.Disadvantage: Influenced by extreme data values.

Measures Of Central Tendency

MEDIAN 3, 14, 20, 27, 14 AND 3, 6, 20, 28, 12, 1The median of a set of numbers is the middle number when the numbers are listed in order of size.Ex,

3, 14, 14, 20, 27 The median is 14 An even number of scores has no middle number. In this case, to find the median add the two middle scores and then divide by 2.Ex,

1, 3, 6, 12, 20, 28 (6 + 12)/2 = 9 The median is 9 Advantage: Not greatly influenced by extreme data values.Disadvantage: No information is given about the sum of the values.

Measures Of Central TendencyMODE 3, 4, 4, 5, 6, 6, 6, 7, 7 The mode is the number that occurs most often.Ex,

3, 4, 4, 5, 6, 6, 6, 7, 7 The mode is 6 There may be more than one mode.Ex, 7, 7, 8, 9, 12, 12, 12, 15, 23, 23, 29, 29, 29, 35 The mode is 12 & 29 Advantages: Easy to locate in frequency tables, graphs, bar graphs, or histograms.Disadvantage: May change greatly with new data values.

Measures Of Central TendencyRANGE 4, 5, 7, 16, 23 The range of a set of data is the difference between the largest and the smallest number in the set. Ex,

4, 5, 7, 16, 23 (23 – 4 = 19) The range is 19 OUTLIERS 68, 72, 76, 69, 83, 5, 74, 85 Outliers are pieces of data that typically lie outside the distribution of reasonable values to such an extent that it is considered an anomaly.Ex,

68, 72, 76, 69, 83, 5, 74, 85 The outlier is 5

Measures Of Central Tendency

Find the mean, median, mode, and the range.45, 24, 99, 76, 84, 19, 64