9-3 Basics of Statistics (Presentation)

8/6/2019 9-3 Basics of Statistics (Presentation)

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9-3 Basics of Statistics

Unit 9 Probability and Mathematical Induction


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Concepts and Objectives

Basics of Statistics (Obj. #34)

Given a set of data, calculate the mean and standarddeviation

Given a set of data, show by graphing that it is

,

data lies within one standard deviation of the mean


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Statistics

When we have talked about finding probabilities, we

have known what the population is (for example, theremay have been 4 blue marbles and 3 white marbles).

Statistics is concerned with the converse. If you know

,

population is.

Example: Politicians use polling data to predict how

well they will do on election day.


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Statistics

As you should recall, the mean of a population is the

average of the data. To measure how widely scatteredthe data is, we use the standard deviation.

The deviation of one data point is the difference between

.

square root of the sum of the squares of the deviationsdivided by one less than the number of data points.


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Standard Deviation

Example: Find the mean and standard deviation of

97, 63, 85, 90, 72

+ + + +=

97 63 85 90 72mean

5=

407

5= 81.4

( )+ + + +

=

2 2 2 2 215.6 18.4 3.6 8.6 9.4

std.dev.5 1

= 757.2

4 13.7586


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Standard Deviation

Example: Find the mean and standard deviation of

97, 63, 85, 90, 72

To do this in the calculator, enter your data

into L1:~ (1-Var Stats)

= =mean 81.4x

= std.dev. 13.7586Sx


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Normal Distribution

If you measure many values of a quantity, such as

lengths of fish in a lake, or scores on an IQ test, most ofthe values normally lie close to the average. Fewer lie

farther away, and very few are very far away.

.

how frequently each data value

occurred. The actual outline is

quite jagged, but we can draw a

smooth curve such that there arejust as many points above the

curve as missing spaces below.


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Normal Distribution

When the curve is bell-shaped as the figure below is,

the numbers are said to be normally distributedaboutthe mean.

The bell-shaped curve is called the normal distribution

.

Each column is 1 unit wide. The

altitude of each column is the

number of data points in that

column.


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Normal Distribution

If you add the areas of the columns, the sum equals the

total number of data points. But there are as many datapoints above the curve as there are gaps below it. So

you can conclude that the area of the region under the

curve is the total number of data oints.

For normally-distributed data,

about of the points lie within

one standard deviation of the

mean.

2

3


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Normal Distribution

Example: Given the data

82 84 83 82 83 81 85 84 80 85 85 85 8783 82 83 84 83 80 81 83 85 84 80 79

a) Plot a frequency distributionb) Find the mean and the standard deviation of the data

c) Confirm that roughly of the data lie within one

standard deviation of the mean.

2

3


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Normal Distribution


82 84 83 82 83 81 85 84 80 85 85 85 8783 82 83 84 83 80 81 83 85 84 80 79

a) Plot a frequency distributionOn graph paper, set up a pair of axes: thex-axis will

be the data, and they-axis will be the frequency.

The smallest data point is 79, while the largest is 87.

Go through the data and make a dot in the column for

each data point.


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Normal Distribution


82 84 83 82 83 81 85 84 80 85 85 85 8783 82 83 84 83 80 81 83 85 84 80 79

a)

78 79 80 81 82 83 84 85 86 87 88


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Normal Distribution


82 84 83 82 83 81 85 84 80 85 85 85 8783 82 83 84 83 80 81 83 85 84 80 79

b) Clear the old data out of L1:yEnter the data into L1:

Run 1-Var Stats: ~

= 82.92 1.9774Sx


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Normal Distribution Example: Given the data

82 84 83 82 83 81 85 84 80 85 85 85 8783 82 83 84 83 80 81 83 85 84 80 79

MeanStandard

b)

78 79 80 81 82 83 84 85 86 87 88


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Normal Distribution Example: Given the data

82 84 83 82 83 81 85 84 80 85 85 85 8783 82 83 84 83 80 81 83 85 84 80 79

MeanStandard

c) There are 16 data

points within 1

standard deviation.

( ) =2 2

25 163 3

78 79 80 81 82 83 84 85 86 87 88


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Homework Algebra & Trigonometry(green book)

Page 698: 1-4 (omit 3c and 4c) Turn-in: all

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9-3 Basics of Statistics (Presentation)