Welcome to IRSC’s LIVE Virtual Lesson on: Mean, Median, Mode, and Range Instructor: Mrs. DiMartino

How to participate in this session:

What you will learn today: How to define and compute: a) the mean b) the median c) the mode d) the range… of a set of data.

Why learn these skills? We use statistics such as the mean, median, mode, and range to obtain information about a population (group) from our sample set of observed values (data).

The mean is the “average” of a set of numbers.  

In other words, it is the sum divided by the count. How to find the mean? Add up all the numbers. 2. Then, divide by how many numbers there are. In other words, it is the sum divided by the count.

Example 1: Finding the Mean What is the mean of these numbers? 6, 11, 7 Add the numbers: 6 + 11 + 7 = 24 Divide by how many numbers there are (3): 24 / 3 = 8 The Mean is: 8

Example 2: Finding the Mean What is the mean of these numbers? 94, 88, 100, 65, 89, 70 Add the numbers: 94 + 88 + 100 + 65 + 89 + 70= 506 2. Divide by how many numbers there are (6): 506 / 6 = 84.3 The mean is : 84.3

Example 3: Finding the Mean What is the mean of these numbers? $24.00, $16.00, $ 18.00, $34.00 1. Add the numbers. $24.00 + $16.00 +$ 18.00 + $34.00 = $92.00 2. Divide the total by how many there are. $92.00/4 = $23.00 The mean is: 23

Median The median is the "middle number" in a list of numbers that have been sorted by value.

How to find the median? 1. Place the numbers you are given in value order. 2. Find the middle number.

Example 1: Finding the Median Find the median of: { 6, 3, 7, 9, 4} Place the numbers you are given in value order. { 3, 4, 6, 7, 9} Find the middle number. { 3, 4, 6, 7, 9} The median is : 6

Example 2: Finding the median Find the median of: { 12, 2, 6, 9, 7, 8} Place the numbers you are given in value order. { 2, 6, 7, 8, 9, 12} Find the middle number. { 2, 6, 7, 8, 9, 12} Wait a minute! There isn’t a middle number!!!

Median (Ex:2 continued) When there are two numbers in the middle… Locate the two middle numbers. (7 and 8) Add them together. 8 + 7 = 15 Divide that number by 2. 15 / 2 = 7 ½ The median is : 7 ½

Example 3: Finding the Median Find the median of: {4, 9, 5, 13, 7} Place the numbers you are given in value order. {4, 5, 7, 9, 13} Find the middle number. {4, 5, 7, 9, 13} The median is : 7

The mode is simply the number that appears most often.

How to Find the Mode? First, put the numbers in order. Then count how many there are of each number. Find the most frequently occurring number.

Example 1: Finding the Mode Find the mode of these numbers: { 3, 6, 7, 8, 7, 3, 2, 7, 9} First, put the numbers in order. { 2, 3, 3, 6, 7, 7, 7, 8, 9} Then count how many there are of each number. Which number occurred most frequently? { 2, 3, 3, 6, 7, 7, 7, 8, 9} The mode is: 7

Example 2: Finding the Mode (when there is more than 1 mode) Find the mode of these numbers: {3, 3, 2, 3, 6, 4, 8, 6, 6, 4} First, put the numbers in order. {2, 3, 3, 3, 4, 4, 6, 6, 6, 8} Then count how many there are of each number. Which number occurred most frequently? {2, 3, 3, 3, 4, 4, 6, 6, 6, 8} The modes are: 3 and 6

Example 3: Finding the Mode Find the mode of these numbers: {12, 9, 11, 6, 4, 3, 12, 8, 9, 12 } First, put the numbers in order. {3, 4, 6, 8, 9, 9, 11, 12, 12, 12 } Then count how many there are of each number. Which number occurred most frequently? The mode is: 12

Range The "range" is the difference between the largest and smallest values (numbers) of a set.

How to find the range? First, put the numbers in order. Locate the largest number and the smallest number. Then subtract them to find the range.

Example 1: Finding the Range Find the range of this set of numbers: {4, 2, 6, 9, 7, 15, 3, 5, 6} First, put the numbers in order. { 2, 3, 4, 5, 6, 6, 9, 7, 15 } 2. Locate the largest number and the smallest number. 15 and 2 3. Then subtract them to find the range. 15-2 = 13

Example 2: Finding the range Find the range of this set of numbers: {22, 16, 17, 8, 12 } First, put the numbers in order. {8, 12, 16, 17, 22 } 2. Locate the largest number and the smallest number. 22 and 8 3. Then subtract them to find the range. 22-8 = 14

Example 3: Finding the Range Find the range of this set of numbers: {1, 3, 9, 4, 20, 6 } First, put the numbers in order. {1, 3, 4, 6, 9, 20} 2. Locate the largest number and the smallest number. 20 and 1 3. Then subtract them to find the range. 20-1 = 19

Word Problem Practice A marathon race was completed by 5 runners. What is the range of times given in hours below? 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr Solution: 1. Order the data from least to greatest. 2.7, 3.5, 4.9, 5.1, 8.3 2. Subtract the highest and lowest. 8.3 hr - 2.7 hr = 5.6 hr Answer: The range of times is 5.6 hrs.

Word Problem Practice On a frigid, winter day in February, the temperature for 8 cities in Maine was recorded. What is the mode of these temperatures?   -8,  0,  -3,  4,  12,  0,   -1,  0 Solution:   1. Order the data from least to greatest.   -8,  -3,  -1,  0,  0,  0,  4,  12 Count how many there are of each number. Then, find the most frequently occurring number. -8,  -3,  -1,  0,  0,  0,  4,  12 Answer:   The mode of these temperatures is 0.

Word Problem Practice In the first 9 weeks of school, Sarah’s test scores in math were: 94%, 88%, 89%, 78%, and 100%. What is her test average (mean)? Solution:   Order the data from least to greatest. 78%, 88%, 89%, 94%, and 100% Add the numbers. 78% + 88% + 89% + 94% + 100% = 449 Divide the total by how many there are (5). 449 / 5 = 89.8%   Answer: The mean is 89.8%

Word Problem Practice Jimmy's phone calls lasted 20 min., 7 min., 9 min., 12 min., and 8 min. He took data to show how long his phone calls typically were. Find the median value of his set of data. Solution:   Order the data from least to greatest. 7 min., 8min., 9 min., 12 min., and, 20 min. 2. Find the middle number. The median is : 9 min.

Type your questions in the chat window please for whiteboard practice. Any Questions? Type your questions in the chat window please for whiteboard practice.

Print your participant Window. Why? To email to your instructor as proof of attendance. To get 1 hour of credit towards your 10 hours this week. How? Place your cursor and left click your mouse on the participant window. On your keyboard, hold down the SHIFT and PRINT SCREEN keys. Then open a Word document and paste (Ctrl + V). Last, attach your word document to an email and send it to your instructor.

Final Comments This session has been recorded for you to play back and view at any time. If you have any questions regarding this topic at a later time, don’t hesitate to contact your instructor. Don’t forget to use the Smarthinking tutor feature within your class site. A tutor is available to you 24 hours a day.

Thank you for coming! I hope you will take advantage of our future LIVE virtual lessons and will attend some of those sessions as well. Have a great day!