mean, median, mode & rangeusa_jeen/mean median mode.pdf · mean = median = mode. ... – it’s...

Mean, Median, Mode

To practice more, or to go for more help, then try some of

these websites!http://www.bbc.co.uk/schools/revisewise/

maths/data/12_act.shtmlhttp://www.mathgoodies.com/lessons/toc

_vol8.shtmhttp://math.about.com/library/weekly/aa0

20502a.htm

http://www.bbc.co.uk/schools/revisewise/maths/data/12_act.shtml�

http://www.bbc.co.uk/schools/revisewise/maths/data/12_act.shtml�

http://www.mathgoodies.com/lessons/toc_vol8.shtm�

http://www.mathgoodies.com/lessons/toc_vol8.shtm�

http://math.about.com/library/weekly/aa020502a.htm�

http://math.about.com/library/weekly/aa020502a.htm�

Definition

• Mean – the average of a group of numbers.

2, 5, 2, 1, 5Mean = 3

Mean is found by evening out the numbers

2, 5, 2, 1, 5

Copyright © 2000 by Monica Yuskaitis


2, 5, 2, 1, 5



2, 5, 2, 1, 5mean = 3


How to Find the Mean of a Group of Numbers

• Step 1 – Add all the numbers.

8, 10, 12, 18, 22, 26

8+10+12+18+22+26 = 96



• Step 2 – Divide the sum by the number of addends.

8, 10, 12, 18, 22, 268+10+12+18+22+26 = 96

How many addends are there?



• Step 2 – Divide the sum by the number of addends.

6)96 sum# of addends1

636

6

63



The mean or average of these numbers is 16.

8, 10, 12, 18, 22, 26


Definition

Medianis in theMiddle


Definition

• Median – the middle number in a set of ordered numbers.

1, 3, 7, 10, 13Median = 7


How to Find the Median in a Group of Numbers

• Step 1 – Arrange the numbers in order from least to greatest.

21, 18, 24, 19, 27

18, 19, 21, 24, 27



• Step 2 – Find the middle number.

21, 18, 24, 19, 27

18, 19, 21, 24, 27



• Step 2 – Find the middle number.

18, 19, 21, 24, 27

This is your median number.



• Step 3 – If there are two middle numbers, find the mean of these two numbers.

18, 19, 21, 25, 27, 28



• Step 3 – If there are two middle numbers, find the mean of these two numbers.

21+ 25 = 46

2) 46 23 median


What is the median of these numbers?

16, 10, 7

10

7, 10, 16



29, 8, 4, 11, 19

114, 8, 11, 19, 29



31, 7, 2, 12, 14, 19

132, 7, 12, 14, 19, 31

12 + 14 = 26 2) 26



53, 5, 81, 67, 25, 78

6053 + 67 = 120 2) 120

5, 25, 53, 67, 78, 81


Definition

Modeis the most

Popular


Definition• A la mode – the most popular or that which is in fashion.

Baseball caps are a la mode today.


Definition• Mode – the number that appears most frequently in a set of numbers.

1, 1, 3, 7, 10, 13Mode = 1


How to Find the Mode in a Group of Numbers

• Step 1 – Arrange the numbers in order from least to greatest.

21, 18, 24, 19, 18 18, 18, 19, 21, 24


How to Find the Mode in a Group of Numbers

• Step 2 – Find the number that is repeated the most.

21, 18, 24, 19, 18 18, 18, 19, 21, 24


Which number is the mode?

29, 8, 4, 8, 19

84, 8, 8, 19, 29



1, 2, 2, 9, 9, 4, 9, 10

91, 2, 2, 4, 9, 9, 9, 10



22, 21, 27, 31, 21, 32

2121, 21, 22, 27, 31, 32

Now YOU try it!!!This is the Stat Family!

Dad Mom Jack Alex Katie

34 33 5 5 1

http://www.barrysclipart.com/barrysclipart.com/showphoto.php?photo=28871&size=big&papass=&sort=1&thecat=160�




MeanHere 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!

MeanRemember, to find the mean, we have to first add up all of the numbers.

34+33+5+5+1= 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

MedianHere are the ages again…Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1

What is the Median?

Remember… Median is the MIDDLE NUMBER


MedianRemember, to find the mean, we have to first

put all of the numbers in order.

34 33 5 5 1

The Mean in this case is 5

ModeHere are the ages again…Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1

What is the Mode?

Remember… Mode is the MOST FREQUENT


ModeRemember, to find the mode, we have to

first put all of the numbers in order.

34 33 5 5 1

The Mode in this case is 5

ความสัมพันธระหวาง คาเฉลี่ย มัธยฐาน ฐานนิยม

Mean = Median = Mode

ความสัมพันธระหวาง คาเฉล่ีย มัธยฐาน ฐานนิยม

Presenter

Presentation Notes

Mode Median Mean

ความสัมพันธระหวาง คาเฉล่ีย มัธยฐาน ฐานนิยม

Presenter

Presentation Notes

Mean Median Mode

Mean, Median, and Mode

• Sometimes you get very similar results with all three.

• Like when you have a normal distribution.

Values

Freq

uenc

y

-4 -2 0 2 4

0.0

0.1

0.2

0.3

Mean

• Usually the mean is preferred:– It uses all the scores (so it’s representative of the

entire data set).

– It’s used to compute the variance and SD.

– It’s good for inferential statistics.

– Note that you should have interval or ratio data to compute a mean.

Median

• Use the median when you have extreme scores or a skewed distribution.

V a lu e s

Frequen

cy

0 .0 0 .2 0 .4 0 .6 0 .8 1 .0

0.00.5

1.01.5

2.0

Median

• Use the median when you have extreme scores or a skewed distribution.

• EXAMPLE:

• X = 10, 11, 11, 11, 11, 12, 12, 13, 13, 100

• M = 20.3

• Median = 11.5

• Median represents most of the distribution best.

Median

• In psychology, you might encounter an open-ended distribution like this:

• N = 20

• Cannot compute a mean.

• Median = 1.5

• Use the median!

Number of Children

Frequency

5 or more 34 23 22 31 60 4

Median

• Use the median if you have ordinal data.

• Remember, the mean balances distance.

• With ordinal data you don’t have equal distances between data points.

Mode

• Use the mode if you have nominal data.

• EXAMPLE:

• Hair color: – 1= brown

– 2 = black

– 3 = blond

– 4 = red

Hair color Frequency4 23 42 51 7

N = 18

Mode

• If you have a discrete variable like number of children, you can compute a mean.

• In this case, means are fractional values that can’t really exist. EXAMPLE: “The average family has 2.5 kids.”

• The mode identifies the typical case: – “The typical family has 2 kids.”– “The modal age for spinal cord injury is 19.”

When to Use the Mean, Median, and Mode

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