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# Modeling Distributions of Data

Chapter 2

by

Tweet## taylor leblanc

on 24 January 2013#### Transcript of Modeling Distributions of Data

In this chapter, we learned about describing and identifying normal distributions and how to do standard normal calculations. Cumulative Relative Frequency Graphs Allows you to examine location within a distribution.

Helps you estimate & interpret the percentile of a distribution. Normal Distribution Described by a normal curve

specified by mean & standard deviation

Mean is the center of the symmetric normal curve Two ways to measure the position within a distribution Percentiles:

Is the value with p percent of the observations less than it.

Z-Score ( Standard Value):

•A measure that quantifies the distance a data point is from the mean of a data set. Chapter 2:

Modeling Distributions of Data Empirical Rule (68-95-99.7 Rule) Density Curve Has an area of 1 underneath curve

Always on or above the horizontal axis

Describes the overall pattern of a distribution Normal Density Curve

(Bell Shaped Density Curve)

(Symmetric Density Curve) Skewed Right Density Curve Skewed Left Density Curve Median & Mean of a Density Curve Median:

is the equal area point

point that divdes the area under the curve in half

Mean:

Balance point

Which the curve would balance if made of solid material Mean& Median The long tail pulls the mean to the right. The long tail pulls the mean to the left 68% of the observations fall within of the mean

95% of the observation falls within 2 of the mean

99.7% of the observation falls within 3 of the mean

mean of 0

Standard deviation of 1 Standard Normal Distribution 80th percentile 1. Plot the data using a graph: dotplot

stemplot

histogram 2. Figure out the pattern: Shape

Outliers

Center

Spread 3. Calculate a numerical summary to briefly describe center & spread 4. Sometimes a pattern of large number observations can be described as a smooth curve Abbreviate the Normal Distribution with mean & standard deviation as

N( , ) 0 + - = 9 8 7 1 2 3 4 5 6 c Standard Normal Distribution Is the normal distribution with a mean of 0 & standard deviation of 1. N(0,1) Using the

Standard Normal Table Is a table of areas under the standard deviation The table entry for each value is the area under the curve to the left of z. How to Solve Problems Involving Normal Distributions State:

Express the problem

Plan:

Draw distribution & shade area of interest under curve

Do:

calculations,

Conclude:

Write conclusion Transforming Data When adding or subtracting the same number (p) to each observation:

(p) would also be added or subtracted to the mean, median, quartiles, percentiles.

This would not change the shape or spread. Transforming Data When multiplying or dividing the same number (p) to each observation:

(p) would also be multiplied or divided to mean, median, quartiles, percentiles & the spread.

This would not change the shape.

Full transcriptHelps you estimate & interpret the percentile of a distribution. Normal Distribution Described by a normal curve

specified by mean & standard deviation

Mean is the center of the symmetric normal curve Two ways to measure the position within a distribution Percentiles:

Is the value with p percent of the observations less than it.

Z-Score ( Standard Value):

•A measure that quantifies the distance a data point is from the mean of a data set. Chapter 2:

Modeling Distributions of Data Empirical Rule (68-95-99.7 Rule) Density Curve Has an area of 1 underneath curve

Always on or above the horizontal axis

Describes the overall pattern of a distribution Normal Density Curve

(Bell Shaped Density Curve)

(Symmetric Density Curve) Skewed Right Density Curve Skewed Left Density Curve Median & Mean of a Density Curve Median:

is the equal area point

point that divdes the area under the curve in half

Mean:

Balance point

Which the curve would balance if made of solid material Mean& Median The long tail pulls the mean to the right. The long tail pulls the mean to the left 68% of the observations fall within of the mean

95% of the observation falls within 2 of the mean

99.7% of the observation falls within 3 of the mean

mean of 0

Standard deviation of 1 Standard Normal Distribution 80th percentile 1. Plot the data using a graph: dotplot

stemplot

histogram 2. Figure out the pattern: Shape

Outliers

Center

Spread 3. Calculate a numerical summary to briefly describe center & spread 4. Sometimes a pattern of large number observations can be described as a smooth curve Abbreviate the Normal Distribution with mean & standard deviation as

N( , ) 0 + - = 9 8 7 1 2 3 4 5 6 c Standard Normal Distribution Is the normal distribution with a mean of 0 & standard deviation of 1. N(0,1) Using the

Standard Normal Table Is a table of areas under the standard deviation The table entry for each value is the area under the curve to the left of z. How to Solve Problems Involving Normal Distributions State:

Express the problem

Plan:

Draw distribution & shade area of interest under curve

Do:

calculations,

Conclude:

Write conclusion Transforming Data When adding or subtracting the same number (p) to each observation:

(p) would also be added or subtracted to the mean, median, quartiles, percentiles.

This would not change the shape or spread. Transforming Data When multiplying or dividing the same number (p) to each observation:

(p) would also be multiplied or divided to mean, median, quartiles, percentiles & the spread.

This would not change the shape.