Презентация Measures of variation. Week 4 (1) онлайн
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- Для класса:1,2,3,4,5,6,7,8,9,10,11
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Слайды и текст к этой презентации:
№1 слайд
Содержание слайда: BBA182 Applied Statistics
Week 4 (1)Measures of variation
Dr Susanne Hansen Saral
Email: susanne.saral@okan.edu.tr
https://piazza.com/class/ixrj5mmox1u2t8?cid=4#
www.khanacademy.org
№2 слайд
Содержание слайда: Numerical measures to describe data
№3 слайд
Содержание слайда: Interquatile range, IQR
Alternative way to calculate the IQR
Khan Academy
№4 слайд
Содержание слайда:
№5 слайд
Содержание слайда: Five-Number Summary of a data set
№6 слайд
Содержание слайда: Five-Number Summary: Example
№7 слайд
Содержание слайда: Exercise
Consider the data given below:
110 125 99 115 119 95 110 132 85
a. Compute the mean.
b. Compute the median.
c. What is the mode?
d. What is the shape of the distribution?
e. What is the lower quartile, Q1?
f. What is the upper quartile, Q3?
g. Indicate the five number summary
№8 слайд
Содержание слайда: Exercise
Consider the data given below.
85 95 99 110 110 115 119 125 132
a. Compute the mean. 110
b. Compute the median. 110
c. What is the mode? 110
d. What is the shape of the distribution? Symmetric, because mean = median=mode
e. What is the lower quartile, Q1? 97
f. What is the upper quartile, Q3? 122
g. Indicate the five number summary 85 < 97 < 110 < 122 < 132
№9 слайд
Содержание слайда: Five number summary and Boxplots
Boxplot is created from the five-number summary
A boxplot is a graph for numerical data that describes the shape of a distribution, in terms of the 5 number summary.
It visualizes the spread of the data in the data set.
№10 слайд
Содержание слайда: Five number summary and Boxplots
Boxplot is created from the five-number summary
The central box shows the middle half of the data from Q1 to Q3, (middle 50% of the data) with a line drawn at the median
Two lines extend from the box. One line is the line from Q1 to the minimum value, the other is the line from Q3 to the maximum value
A boxplot is a graph for numerical data that describes the shape of a distribution, like the histogram
№11 слайд
Содержание слайда: Five number summary and boxplot
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5
Minimum number = 1
Maximum number = 5
= 1
2.5
Median = 2
Five number summary: 1 = 1 < 2 < 2.5 < 5 (plot a dot chart, then boxplot)
№12 слайд
Содержание слайда: Five number summary and boxplot
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120
Minimum number = 1
Maximum number = 120
= 1
2.5
Median = 2
Five number summary: 1 = 1 < 2 < 2.5 < 120
№13 слайд
Содержание слайда: Boxplot
№14 слайд
Содержание слайда: Gilotti’s Pizza Sales in $100s
№15 слайд
Содержание слайда: Gilotti’s Pizza Sales
What are the shapes of the distribution of the four data set?
№16 слайд
Содержание слайда: Gilotti’s Pizza Sales - boxplot
№17 слайд
Содержание слайда: Gilotti’s Pizza Sales in $100s
№18 слайд
Содержание слайда: Measuring variation in a data set
that follows a normal distribution
№19 слайд
Содержание слайда: Measuring variation in a data set
Data set 1 : 23 19 21 18 24 21 23 Mean: 21.3
Data set 2 : 23 35 19 7 21 24 22 Mean: 21.6
Which of these two data sets has the highest spread/variation? Why?
№20 слайд
Содержание слайда: Average distance to the mean:
Standard deviation
Most commonly used measure of variability
Measures the standard (average) distance of each individual data point from the mean.
№21 слайд
Содержание слайда: Calculating the average distance to the mean
Our goal is to measure the standard distance of each single data in the data set from the mean.
1st step: Calculate the mean of the data set =
2nd step: Calculate the standard distance from the mean is to determine distance from the
mean for each individual score:
deviation score = X - μ
Where x is the value of each individual score and μ the population mean.
№22 слайд
Содержание слайда: Calculating the average distance to the mean
Step 3: Once we have calculated the distance between each single score and the mean, we add up the those deviation scores. Our mean in this example is = 3.
Example: We have a set of 4 scores (): 8, 1, 3, 0,
№23 слайд
Содержание слайда: Calculating the average distance to the mean
Notice that the deviation score adds up to zero!
This is not surprising because the mean serves as balance point (middle point) for the distribution. (!Remember: In a symmetric distribution the mean and the median are identical)
The distances of the single score above the mean equal the distances of the single scores below the mean.
Therefore the deviation score always adds up to zero.
№24 слайд
Содержание слайда: Calculating the average distance to the mean
Step 3: The solution is to get rid of the + and – which causes the cancelling out effect. We square each deviation score and sum them up
№25 слайд
Содержание слайда: Population Variance,
Average of squared deviations from the mean
Population variance:
№26 слайд
Содержание слайда: Sample Variance,
Average of squared deviations from the mean
Sample variance:
№27 слайд
Содержание слайда: Population Standard Deviation,
Most commonly used measure of variation in a population
Shows variation about the mean in a symmetric data set
Has the same units as the original data,
Example: If original data is in meters than the standard deviation will also be in meters.
Population standard deviation:
№28 слайд
Содержание слайда: Sample Standard Deviation, s
Most commonly used measure of variation in a sample
Shows variation about the mean
Has the same units as the original data
Sample standard deviation:
№29 слайд
Содержание слайда: Calculation Example:
Sample Standard Deviation, s
№30 слайд
Содержание слайда: Class example
Calculating sample variance and standard deviation
Compute the variance, and standard deviation, s, of the following sample data:
6 8 7 10 3 5 9 8
№31 слайд
Содержание слайда: Class example (continued)
When we analyze the variance formula we, see that we need to calculate the sample mean, first:
= = 7
№32 слайд
Содержание слайда: Class example (continued)
The mean = 7
№33 слайд
Содержание слайда: C Class example (continued)
Calculating the sample variance: 6 8 7 10 3 5 9 8
=
= = 5.14
Sample standard deviation, s = 2.27 (average distance to the mean of 7)
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