Normal or skewed distributions (descriptive both2)

1. Are the distributions all normal or is at least
one skewed?
Normal? Skewed?

2. The Normal Distribution is a distribution that has most
of the data in the center with decreasing amounts
evenly distributed to the left and the right.
Skewed Distribution is distribution with data clumped
up on one side or the other with decreasing amounts
trailing off to the left or the right.
Central Tendency, Spread, or Symmetry?

3. The Normal Distribution is a distribution that has most
of the data in the center with decreasing amounts
evenly distributed to the left and the right.
The Skewed Distribution is distribution with data
clumped up on one side or the other with decreasing
amounts trailing off to the left or the right.
Central Tendency, Spread, or Symmetry?
Right skewed Left skewed

4. Why is this important to know?

5. Why is this important to know?
The six statistics you are about to learn are
measures of central tendency – the mean, the
median, and the mode.
Along with measures of spread – the range,
standard deviation, and interquartile range.
The mean and the standard deviation are best used
in a normal distribution. The median and the
interquartile range are best used with skewed
distributions.

6. Why is this important to know?
The six statistics you are about to learn are
measures of central tendency – the mean, the
median, and the mode.
Along with measures of spread – the range,
standard deviation, and interquartile range.
The mean and the standard deviation are best used
in a normal distribution. The median and the
interquartile range are best used with skewed
distributions.

7. Why is this important to know?
The six statistics you are about to learn are
measures of central tendency – the mean, the
median, and the mode.
Along with measures of spread – the range,
standard deviation, and interquartile range.
The mean and the standard deviation best describe
the nature of a normal distribution. The median
and the interquartile range are best used with
skewed distributions.

8. Why is this important to know?
The six statistics you are about to learn are
measures of central tendency – the mean, the
median, and the mode.
Along with measures of spread – the range,
standard deviation, and interquartile range.
The mean and the standard deviation best describe
the nature of a normal distribution. Whereas, the
median and the interquartile range best describe
skewed distributions.

9. Why is this important to know?
The six statistics you are about to learn are
measures of central tendency – the mean, the
median, and the mode.
Along with measures of spread – the range,
standard deviation, and interquartile range.
The mean and the standard deviation best describe
the nature of a normal distribution. Whereas, the
median and the interquartile range best describe
skewed distributions.
This will be explained in more
detail in another part of the
decision model

10. How can you tell if a distribution is
• Normal?
or
• Skewed?

11. There are two ways to check for skew:

12. There are two ways to check for skew:
1. When you have one sample: For example - What is the
average test score for Mr. Edwards class?
and
2. When you have two samples: Who has the highest test score
average – Mr. Edwards or Mrs. Jones classes?

13. There are two ways to check for skew:
1. When you have one sample: For example - What is the
average test score for Mr. Edwards class?
and
2. When you have two samples: Who has the highest test score
average – Mr. Edwards or Mrs. Jones classes?
Mr. Edwards class test score distribution
Low scores
Most scores
High scores

14. There are two ways to check for skew:
1. When you have one sample: For example - What is the
average test score for Mr. Edwards class?
and
2. When you have two samples: For example - Who has the
highest test score average – Mr. Edwards or Mrs. Jones
classes?
Mr. Edwards class test score distribution
Low scores
Most scores
High scores

15. There are two ways to check for skew:
1. When you have one sample: For example - What is the
average test score for Mr. Edwards class?
and
2. When you have two samples: For example - Who has the
highest test score average – Mr. Edwards or Mrs. Jones
classes?
Mr. Edwards class test score distribution
High scores
Low scores
Most scores
Mr. Edwards class test score distribution
High scoresLow scores
Most scores
Mrs. Jones class test score distribution
Low scores
High scores

16. To learn how to calculate and interpret the skew
for:
one sample click here.
two samples click here
When you complete these two tutorials you will
be ready to go on.

17. Let’s Practice!

18. Is there at least one distribution that is skewed
or are all normal?
Normal? Skewed?

19. Is there at least one distribution that is skewed
or are all normal?
A golf coach wants to know the average forearm
circumference of his golf team players.
Normal? Skewed?

20. Is there at least one distribution that is skewed
or are all normal?
A golf coach wants to know the average forearm
circumference of his golf team players.
Here is the output for skew:
Normal? Skewed?
Statistics
Forearm circumference
N Valid 40
Missing 0
Skewness -1.105
Std. Error of Skewness .374

21. Is there at least one distribution that is skewed
or are all normal?
A golf coach wants to know the average forearm
circumference of his golf team players.
Here is the output for skew:
Normal? Skewed?
Statistics
Forearm circumference
N Valid 40
Missing 0
Skewness -1.105
Std. Error of Skewness .374

22. Is there at least one distribution that is skewed
or are all normal?
A golf coach wants to know the average forearm
circumference of his golf team players.
Here is the output for skew:
Normal? Skewed?
Statistics
Forearm circumference
N Valid 40
Missing 0
Skewness -1.105
Std. Error of Skewness .374
-1.105 is
between -2.0
and +2.0

23. Next Problem

24. Is there at least one distribution that is skewed
or are all normal?
Who has a higher IQ – cats or dogs?
Normal? Skewed?

25. Is there at least one distribution that is skewed
or are all normal?
Who has a higher IQ – cats or dogs?
Here’s the output for skew:
Normal? Skewed?
Report
speed
Animal IQ Mean N Std. Deviation Skewness
Std. Error of
Skewness
Cats 72.81 16 6.595 -.953 .564
Dogs 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
-.953 is between -2.0
and +2.0.
Cat IQ distribution is
normal

26. Is there at least one distribution that is skewed
or are all normal?
Who has a higher IQ – cats or dogs?
Here’s the output for skew:
Normal? Skewed?
Report
speed
Animal IQ Mean N Std. Deviation Skewness
Std. Error of
Skewness
Cats 72.81 16 6.595 -.953 .564
Dogs 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409
-2.344 is less than -2.0.
Dog IQ distribution is
skewed left

27. Is there at least one distribution that is skewed
or are all normal?
Who has a higher IQ – cats or dogs?
Here’s the output for skew:
Normal? Skewed?
Report
speed
Animal IQ Mean N Std. Deviation Skewness
Std. Error of
Skewness
Cats 72.81 16 6.595 -.953 .564
Dogs 79.94 17 18.081 -2.344 .550
Total 76.48 33 14.034 -1.832 .409

28. Are the distributions all normal or is at least
one skewed?
Normal? Skewed?