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What is a Distribution?
We will illustrate what a distribution is with a
data set that describes the hours students’ study
Here is the data set:
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Data
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Data Set
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
From this data set we
will create a
distribution:
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
The X Axis, will be the
number of hours of
study
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
The Y Axis, indicates
the number of times
the same number
occurs
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
The Y Axis, indicates
the number of times
the same number
occurs
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
The Y Axis, indicates
the number of times
the same number
occurs
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
The Y Axis, indicates
the number of times
the same number
occurs
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
The Y Axis, indicates
the number of times
the same number
occurs
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
The Y Axis, indicates
the number of times
the same number
occurs
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
Number of Occurrences
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
Student Hours of
Study
Bart 1
Basheba 2
Bella 2
Bob 3
Boston 3
Bunter 3
Buxby 4
Bybee 4
Bwinda 5
Hours of Study
1 2 3 4 5
NumberofOccurrences
1
2
3
This is a
distribution
One way to represent a distribution like this:
One way to represent a distribution like this:
One way to represent a distribution like this:
Is like this:
One way to represent a distribution like this:
Is like this:
One way to represent a distribution like this:
Is like this:
Normal distributions have
the majority of the data in
the middle
One way to represent a distribution like this:
Is like this:
Normal distributions have
the majority of the data in
the middle
One way to represent a distribution like this:
Is like this:
With decreasing
but equal amounts
toward the tails
One way to represent a distribution like this:
Is like this:
With decreasing
but equal amounts
toward the tails
With decreasing
but equal amounts
toward the tails
Distributions can take other forms as well:
Distributions can take other forms as well:

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What is a distribution?

  • 1. What is a Distribution?
  • 2. We will illustrate what a distribution is with a data set that describes the hours students’ study
  • 3. Here is the data set:
  • 4. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5
  • 5. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Data
  • 6. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Data Set
  • 7. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 From this data set we will create a distribution:
  • 8. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5
  • 9. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 The X Axis, will be the number of hours of study
  • 10. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5
  • 11. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5
  • 12. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs
  • 13. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs
  • 14. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs
  • 15. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs
  • 16. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs
  • 17. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs
  • 18. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 Number of Occurrences
  • 19. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences
  • 20. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences
  • 21. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 22. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 23. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 24. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 25. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 26. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 27. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 28. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 29. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 30. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 31. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 32. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 33. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3
  • 34. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3 This is a distribution
  • 35. One way to represent a distribution like this:
  • 36. One way to represent a distribution like this:
  • 37. One way to represent a distribution like this: Is like this:
  • 38. One way to represent a distribution like this: Is like this:
  • 39. One way to represent a distribution like this: Is like this: Normal distributions have the majority of the data in the middle
  • 40. One way to represent a distribution like this: Is like this: Normal distributions have the majority of the data in the middle
  • 41. One way to represent a distribution like this: Is like this: With decreasing but equal amounts toward the tails
  • 42. One way to represent a distribution like this: Is like this: With decreasing but equal amounts toward the tails With decreasing but equal amounts toward the tails
  • 43. Distributions can take other forms as well:
  • 44. Distributions can take other forms as well: