3-2 Measures of Center Day 1

Discussion Consider students’ grades on a math test: 22%, 94%, 95%, 96%, 98%, 99%. The average grade is 84%. Notice how much easier it is to summarize a data set with one number. This is a statistic. It is called a measure of center because it describes the middle of the data set.

Discussion The average isn’t the only statistic that measures the center of a data set. Does anyone know another measure of center? Median

Today’s Objective You will be able to define data and data sets. You will be able to define and calculate mean and median.

Definitions Data – piece of information Data Set - group of data   Data Set - group of data Your grade is a piece of data. Everyone’s grade in your class is a data set. Can you give me another example of data and data set?

Definitions Measure of Center– one value that describes the middle of a data set Examples: Mean, Median

Definitions Mean – average; add up all of the data items, then divide by how many there are Median - middle number when the numbers are in order

Example 1 My siblings’ ages are: 8, 9, 12, 15, 16, 18, 20 8, 9, 12, 15, 16, 18, 20 Take a guess at the mean. Find the mean. Find the median.

Example 2 My cousins ages are: 8, 12, 8, 17, 32, 18, 20, 14 8, 12, 8, 17, 32, 18, 20, 14 Take a guess at the mean. Find the mean. Find the median.

Example 3 Make up a data set with 7 numbers that has the following characteristics: Mean: 8 Median: 6 Set the median. Fill in the rest of the numbers to get the correct mean.

You Try! Guess the mean. Then find the mean and median. 1. 2, 5, 8, 10, 10 2. 7, 9, 12, 2, 11, 7 3. 40, 68, 40, 84, 84, 75

You Try! 4. Make up a data set with 6 numbers with the following characteristics: Mean: 6 Median: 5

What did we learn today? To define data and data sets To define and calculate mean and median

Review Question How do you find the mean? Add them up then divide How do you find the median? Find the middle number

Discussion Previously, we defined and calculated the mean and median of data sets. These values are called measures of center. They are called this because they each describe the middle of a data set. Now, we are going to try to figure out which one best describes a data set.

Discussion Students’ grades on a test: 22%, 94%, 95%, 96%, 98%, 99% Find the mean and median.

Discussion Students’ grades on a test: 22%, 94%, 95%, 96%, 98%, 99% What statement better reflects the classes’ grades? The ‘average’ student received an 84%. The ‘average’ student received a 95.5%.

Discussion Notice by having one low piece of data the mean is affected greatly while the median barely changes. Therefore, we can’t use the mean when we have a data set with an extreme value. This could be an extremely low or high number.

Today’s Objective You will be able to choose the correct measure of center to summarize a data set.

Definitions Outlier – an extreme data value (this could be a extremely low or high number) * Use the mean when the numbers are close together. * Use the median when you have an outlier.

Example 1 Which measure of center would best summarize each of the following data sets? 1. 10, 12, 20, 26, 27, 29 2. 1, 2, 3, 4, 5, 100 3. 100, 120, 180, 200, 240, 300

Example 2 Number of books read by students in a reading class: 1, 1, 2, 2, 3, 3, 4, 55, 64 What is the mean? What is the median? Which statement better reflects the class? The ‘average’ student read 15 books. The ‘average’ student read 3 books. What statistic best summarizes the data set? Why?

Example 2 The principal asked the reading teacher how the reading class was doing. The teacher said awesome! My students are reading 15 books each on average. Would the teacher be lying? misleading? Notice how you can use a statistic to make something look better.

Summarize Write one sentence that describes when we should use the mean. Write one sentence that describes when we should use the median.

You Try! Find the mean and median. Then state whether the mean or median would best describe the data set. 1. 2, 4, 6, 8, 10, 18, 20 2. 5, 5, 10, 20, 50, 1000

What did we learn today? To choose the correct measure of center to summarize a data set