**Mean, Median & Mode**

**Mean, Median & Mode**

Mean

Mean: Average of numbers in a set.

How do you find it?

Step 1: Add the numbers.

18+ 22+14=54

Step 2: Divide the sum by the number

of digits you added.

54÷3=18

The mean of the three digits is 18.

Median

Median: The middle number when all the numbers are listed in order.

12, 14, 11, 11, 9, 16, 17, 19

Put them in order!

2, 9, 11, 11, 12, 14, 16, 17, 19

Which number is in the middle?

2, 9, 11, 11, 12, 14, 16, 17, 19

Since 12 is in the middle, the median is 12.

Mode

Mode: The number that occurs most often in a set of numbers.

12,14,11,11,9,16,17,19,2

Since the number 11 occurs twice,

the mode is 11.

18, 22, 14

Mean Practice

Find the means for the following collection of numbers:

1) 21,24,25,25,22,15

2) 14,16,15,14,18,21

3) 201, 211, 213, 222, 223

4) 4,531; 4,632; 4,111; 4,551

Median Practice

Find the median for the following collection of numbers:

1) 21,24,25,25,22

2) 14,16,15,14,18,21

3) 201, 211, 213, 222, 223

4) 4,531; 4,632; 4,111; 4,551; 4,000

Mode Practice

Find the modes for the following collection of numbers:

1) 21,24,25,25,22,15

2) 14,16,15,14,18,21

3) 201, 211, 213, 222, 222

4) 4,531; 4,632; 4,111; 4,551; 4,531

12,14,11,11,9,16,17,19,2

WAIT!!!!

What if two numbers are in the middle?

9, 11, 11, 12, 14, 16, 17, 19

Find the mean of the two numbers.

12+14=26 26÷2=13

The mean is 13, so the median is 13.

References

Why do we need to know this?

Hey Diddle Diddle Mean Median Mode Range song - YouTube. (n.d.). YouTube. Retrieved June 15, 2013,

Math Forum - Ask Dr. Math. (n.d.). The Math Forum @ Drexel University. Retrieved June 15, 2013, from http://mathforum.org/library/drmath/view/61848.html

Mean, Median, Mode. (n.d.). WyzAnt. Retrieved June 13, 2013, from www.wyzant.com/help/math/elementary_math/mean_median_and_mode

Sellers, T. S. (n.d.). TeachersPayTeachers.com - An Open Marketplace for Original Lesson Plans and Other Teaching Resources. TeachersPayTeachers.com - An Open Marketplace for Original Lesson Plans and Other Teaching Resources. Retrieved June 15, 2013, from http://www.teacherspayteachers.com/

The Mean, Median and Mode Toads - YouTube. (n.d.). YouTube. Retrieved June 15, 2013, from

APA formatting by BibMe.org.

In Class Assignment

Homework

A little ditty, to get stuck in your head and to help you remember!

Mean

Median

Mode

-Averaging Grades

-Averaging Money

-Averaging ...

Finding the median of a set of numbers is similar to finding an average, but it relies less on averaging and more on where the middle number is in the series.

The mode of a series of numbers is the number that appears the most often.

Suppose you interview with a company that has 10 general employees, 7 assistants, 3 managers, and 1 owner. For this company, the mean salary is $400, and the median is also $400. But you are applying for the position of general employee, whose starting salary is $100! Why are the mean and median so far away?

Well, the 10 general employees each make $100. The 7 assistants each make $400, the 3 managers each make $900, and the owner makes $1900. If you do the math to find the median or mean, $400 is the answer (try it!). So what can you do?

The mode is the type of average you want to know in this situation. The mode is the number the occurs most frequently. In the example for median, 6 would be the mode because it occurs twice, while the other numbers each occur once. In our employee example, the mode is $100 because that number occurs ten times, which is more than any other number occurs.

Suppose you are an adult looking for a job. You interview with a company that has ten employees, and the interviewer tells you that the average salary is $200 per day. Wow, that's a lot of money! But that's not what you would be making. For this particular company, you would make half of that. Each employee makes $100 per day, except for the owner, who makes $1100 per day. What? How do they get $200 for average then?!

Well, let's take a look:

Nine employees make $100, so adding those up is 9 x 100 = 900. Then the owner makes $1100, so the total is $1100 + $900 = $2000. Divide by the total number of employees, ten, and we have $2000/10 = $200. Because the owner makes so much more than everyone else, her salary "pulls" the average up.

A better question to ask is, "What is the _median_ salary?" The median is the number in the middle, when the numbers are listed in order. For example, suppose you wanted to find the median of the numbers 6, 4, 67, 23, 6, 98, 8, 16, 37. First, list them in order: 4, 6, 6, 8, 16, 23, 37, 67, 98. Now, which one is in the middle? Well, there are nine numbers, so the middle one is the fifth, which is 16, so 16 is the median.

Now look at those salaries again. To find the median salary, we look at the salaries in order: 100, 100, 100, 100, 100, 100, 100, 100, 100, 1100. This is an even number of salaries, so we look at the middle two. They are both 100, so the median is $100. That's much better at telling you how much you'll make if you accept the job.

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