MEAN

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MEAN

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LET’S CHECK WHAT YOU KNOW

• Simplify1. 3+2+45+67+78+96 =2. (45+67+56+43+23)= 33. 9.261 = 34. 255 ÷ 4 =5. 137 ÷ 5 =

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MEAN

• The MEAN of a set of data is the sum of the data divided by the number of items.

• Mean = sum of data number of items

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Example-1

• Find the mean of the following observations: 41, 80, 112, 86, 21

• Mean = (41+80+112+86+21) 5 = 340 = 68 5

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Example-2

• Find the mean of the following data: 3, 10, 12, 7, 9, 8, 7.

• Mean = Sum of data Number of data = 3+10+12+7+9+8+7 7 = 56 = 8 7

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Mean

• A number that helps describe all of the data in a data set is an average or a measure of central tendency.

• One of the most common measures of central tendency is the mean.

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Outliers

• In statistics, a set of data may contain a value much higher or lower than the other values.

• This value is called an outlier.• Outliers can significantly

affect the mean.

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Example of Outliers

•Identify the outlier in the temperature data. Then find the mean with and without the outlier. Describe how the outlier affects the mean of the data.

Day Temp (°F)

Monday 80

Tuesday 81

Wednesday

40

Thursday 77

Friday 82

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Example of Outliers

•Compared to the other values, 40°F is extremely low. So, it is an outlier.•Mean with outlier

= 80+81+40+77+82

5

= 360

5

=72

•Mean without outlier = 80+81+77+82

4= 320 4=80

With the outlier, the mean is less than all but one of the data values.Without the outlier, the mean better represents the values in the data set

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Your Turn!

•Find the mean for the snowfall data with and without the outlier. Then tell how the outlier affects the mean of the data.

Month Snowfall (in.)

Nov. 20

Dec. 19

Jan. 20

Feb. 17

Mar. 4

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BREAK

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http://www.thekidzpage.com/freekidsgames/games/breakdown/index.html

Have Fun!

Title: Format: WebEx Web BrowserDouble-click to edit

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Do it by yourself

• The marks obtained by 10 students in a test are: 90, 75, 80, 65, 78, 65, 80, 77, 86 and 74. Find the mean.

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Practice Problems

Find the mean of the following:

1. 72,55,48,61,63,372. 75,82,81,95,923. 7,15,9,12,10,134. 365,225,118,132,2405. 15,24,14,48,27,20

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More problems• The marks Christy got in 6

tests are : 65 72, 59, 81, 68, 72. while another student Fredy wrote only 5 of these tests and his marks are 71, 54, 68, 82, 75. Whose overall performance is better?

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Assignments

1. The minimum temperatures in Celsius recorded on various days of a week are 220, 250, 230, 210, 200, 270. Find their arithmetic mean.

2. Calculate the mean weight of the students from the following data: 135, 184, 94, 288, 49, 200

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Assignment 3. The maximum daily temperature (in

C0) for the first week of a month in Melbourne are 37, 35, 38, 34, 39, 36 and 33. calculate the mean temperature for the week.

Find the mean of :4. 3, 7, 8, 5, 6, 9, 6, 4, 65. 25, 31, 27, 29, 32, 25, 28, 25.6 3, 5, 1, 5, 7, 3, 2, 37 2, 3, 4, 4, 1, 6, 4, 3.

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Assignment 8. Which piece of data in the

data set 98, 103, 96, 147, 100, 85, 546, 120, 98 is an outlier?

9. Write a set of data in which the mean is affected by the outlier.

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Let’s Review what we studied today

• Mean of a set of data is the sum of the data divided by the number of items.

• Mean = sum of data number of items

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Thanks!