Remember the 3 Ms? Mean, Median, and Mode ~Central Tendency~

Objective The student will be able to calculate measures of central tendency (mean, median, and mode)

Mean = Average The mean is the average of a data set To find the mean: Find the sum of the data items Divide by the number of data items. The mean will Always be greater than the smallest number and less than the largest number. These are data items: 2, 3, 4, 5, 8, 8, and 12 2 + 3 + 4 + 5 + 8 + 8 + 12 7 (total data items) 42 / 7 = the mean, which is 6

Mean is the average of a set of data Mean is the average of a set of data. To calculate the mean, find the sum of the data and then divide by the number of data.

Central Tendency The Central Tendency is the center of the distribution of a data set. The mean of a set of data is the most common measure of Central Tendency. Other measures are mode and median

A way to remember…Mean – It is very mean because it makes you do all that work! grrrrrrrrr You try the next one!

ABC Warehouse sells flat screen TVs at the following prices: $350, $275, $500, $325, $100, $375, and $300. What is the mean price?

Outliers Values that are much higher or lower than others in a data set are Outliers. High temperatures Monday through Friday were 80, 81, 60, 77, and 82. Identify the outlier in the data.

Median What does this word make you think of… The middle number of a set of data, arranged in numerical order Median is the middle of the road

How Tall are You? Need 5 volunteers: Need 1 more volunteer What is the median height? Need 1 more volunteer What was different about our middle number? Odd Number of Data Items: the middle number when the data items are put in numerical order. Even Number of Data Items: the two middle numbers when data items are put in numerical order.

Median Find the median of this data set 4, 3, 7, 9, 5, 3, 1 Put them in order! There are 7 numbers in total…looking for the “middle” number Median =

Mode What does this word make you think of? Mode: the data item that occurs the MOST What is the mode from our previous data set? 4, 3, 7, 9, 5, 3, 1 3 is a mode for these data items.

How old are you? Raise your hand if you are: 13 14 15 16 What is the mode?

Mean The average Median The number or average of the numbers in the middle Mode The number that occurs most

Find me the M, M & Ms 12, 14, 26, 37, 8, and 14 Re-order: 8, 12, 14, 14, 26, 37, 26. Mean: 19.6 Median: 14 How many Modes: 2 Mode: 14, 26

Find me ONLY Mode: Grape, grape, banana, nectarine, strawberry, strawberry, strawberry, orange, watermelon. How many modes? Just one: strawberry.

Find me the M, M & Ms 2.3, 4.3, 3.2, 2.9, 2.7, and 2.3. Re-order: 2.3, 2.3, 2.7, 2.9, 3.2, 4.3. Mean: 2.95 Median: 2.8 How many Modes? 1 Mode: 2.3

Outlier Outlier: is a data item (data value) that is much higher or lower than the other data values. Outliers can affect the mean of a group of data. Example: 2, 3.5, 1, 2, 5,000,000. Example: 35, 45, 40, 37, -6.

Describing Data with M, M, & M. You can use what you know about Mean, Median, and Mode to describe data. But figuring out which M describes it best is difficult. I think mode describes it best! Nah! Its got to be mean!

Which M, M, & M is best? The favorite movie of students in the eighth grade class? Mode: good for non-numerical data items and for frequent occurrences.

Which M, M, & M is best? The distances students in your class travel to school. Median: one student may live much further than everyone else. When an outlier may significantly influence the mean, we use median.

Which M, M, & M is best? The daily high temperature during a week in July. Mean: since daily temp. are not likely to have outlier, mean is best. When data have no outlier, use mean.

Measures and Central Tendency Your text book is going to ask you determine which MEASURE of CENTRAL TENDENCY best describe the data. Its just asking you to figure out which M works with the data best!