Measures of Central Tendency: Mean, Median, Mode and Range

YOUR FOCUS GPS Standard: M6D1cd Students will represent and analyze data by examining variations within and between groups and relating data analysis to the content of the question posed. EU: We can analyze data in many ways to determine differences between groups. EQ: How can I use my data to compare groups? Vocabulary: Mean, Median, Mode, Range

The residents of Whateverville need your help! Mayor Wallop, a scientist, has invented a weather machine. Now he's in control of the weather for the entire region and has subjected the residents of Whateverville to so many different temperatures that they don't know what season it is. One day it's snowing; the next day it's over 100 degrees! The plants are dying, and people are getting sick. Take a look at the temperatures in the past week. Sunday50° Monday62° Tuesday90° Wednesday106° Thursday10° Friday50° Saturday0°

The first step to helping the residents of Whateverville solve this problem is to put the temperatures in order from least to greatest. Sunday50° Monday62° Tuesday90° Wednesday106° Thursday10° Friday50° Saturday0°

What is the highest temperature this week? What is the lowest temperature this week? What is the difference between the highest and lowest temperature?

This is your RANGE The range is the difference between the highest and the lowest numbers of the series. All we have to do is put the numbers in order and subtract the lowest from the highest! = 106

Take a look at your temperatures ordered from least to greatest. What temperature is in the middle?

This is your MEDIAN The Median is the middle value on the list. The first step is to always to put the numbers in order. 0° 10° 50° 50° 62° 90° 106°

Median Example #2 Now, let’s try it with an even number of temperatures 0° 10° 50° 50° 62° 90° 94° 106° This time, there are two numbers in the middle, 50° and 62° 0° 10° 50° 50° 62° 90° 94° 106° Now we will need to find the Average of these two numbers, by adding them and dividing by two = ÷2= 56 Here, the Median is 56

What is the temperature that occurs most frequently?

This is your MODE The Mode refers to the number that occurs the most frequently. It’s easy to remember… the first two numbers are the same! MOde and MOst Frequently! 0° 10° 50° 50° 62° 90° 106°

How can you find the average of the temperatures?

This is your MEAN The mean is the Average of a group of numbers It is helpful to know the mean because then you can see which numbers are above and below the mean

Mean Example To find the Mean, first you must add up all of the numbers = 368 Now, since there are 7 temperatures, we will next divide the sum by ÷7 = 52.6 We will round to the nearest whole number. So, the Mean is 53

Mayor Wallop hears the complaints of the residents, and for the next 10 days he tries to adjust his temperatures to the average spring temperature in the region. Sunday 48° Monday 45° Tuesday 63° Wednesday 51° Thursday 101° Friday 69° Saturday 55° Sunday 62° Monday 53° Tuesday 57°

Calculate the mean, median, mode, and range for these new temperatures. Sunday 48° Monday 45° Tuesday 63° Wednesday 51° Thursday 101° Friday 69° Saturday 55° Sunday 62° Monday 53° Tuesday 57°

Try this one!!! This is the Stat Family! DadMomJackAlex Katie

Mean Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Mean? Remember… Mean is the AVERAGE Try it on your paper and see what you come up with!

Mean Remember, to find the mean, we have to first add up all of the numbers = 80 Then, since there are 6 people in the family, we next divide by 6. 78÷6= 13 The Mean in this case is 13

Median Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Median? Remember… Median is the MIDDLE NUMBER Try it on your paper and see what you come up with!

Median Remember, to find the mean, we have to first put all of the numbers in order The Mean in this case is 5

Mode Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Mode? Remember… Mode is the MOST FREQUENT Try it on your paper and see what you come up with!

Mode Remember, to find the mode, we have to first put all of the numbers in order The Mode in this case is 5

Range Here are the ages again… Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1 What is the Range? Remember… Range is the DIFFERENCE Try it on your paper and see what you come up with!

Range Remember, to find the range, we have to first put all of the numbers in order The highest age is 34, and the lowest is 1 Now we need to subtract to find the difference 34-1= 33 The range is 33