1. Sections 2.3 and 2.4

2. Quiz 2.3 – 2.4 tomorrow
(or next school day)
-May use 1 side of a 4 x 6 note card for the quiz

3. Percentiles and Cumulative Relative Frequency Plots
Percentiles measure position within a data set.

4. Percentiles and Cumulative Relative Frequency Plots
Percentiles measure position within a data set.
Q1 is 25th percentile - - the value that separates the lowest 25% of the ordered values from the rest
Median is ______ percentile

5. Percentiles and Cumulative Relative Frequency Plots
Percentiles measure position within a data set.
Q1 is 25th percentile - - the value that separates the lowest 25% of the ordered values from the rest
Median is 50th percentile
Q3 is the _____ percentile

6. Percentiles and Cumulative Relative Frequency Plots
Percentiles measure position within a data set.
Q1 is 25th percentile - - the value that separates the lowest 25% of the ordered values from the rest
Median is 50th percentile
Q3 is the 75th percentile

7. Percentiles and Cumulative Relative Frequency Plots
In general, a value is at the kth percentile if k% of all values are less than or equal to it.

9. Suppose you have a set of univariate data (data that involves a single variable per case).
The data consists of the weights of the students in a class.
What are the cases?
What is the variable?

10. Suppose you have a set of univariate data (data that involves a single variable per case).
The data consists of the weights of the students in a class.
What are the cases? Individual students
What is the variable?

11. Suppose you have a set of univariate data (data that involves a single variable per case).
The data consists of the weights of the students in a class.
What are the cases? Individual students
What is the variable? The weight for each student

12. The data consists of the weights of the students in a class.
List all the measures you know to describe the data set.
Hint: Should list 11 measures

13. List all the measures you know to describe the data set.
x, sx, median, Q1, Q3, min, max, range, IQR, mode, and outliers

14. List all the measures you know to describe the data set.
x, sx, median, Q1, Q3, min, max, range, IQR, mode, and outliers
Now categorize these measures in terms of describing shape, center, or spread.

15. List all the measures you know to describe the data set.
x, sx, median, Q1, Q3, min, max, range, IQR, mode, and outliers
Now categorize these measures in terms of describing shape, center, or spread.
None of these alone describe the shape.

16. How do you describe the shape?

17. How do you describe the shape?
uniform
normal distribution
skewed left or right
bimodal

18. Page 80, P28

19. P28 (Rescaling) (a) converting height from inches to feet is rescaling
Which measures are affected by rescaling?

20. P28 (Rescaling) (a) converting height from inches to feet is rescaling
Which measures are affected by rescaling?
mean
median
standard deviation
and IQR

21. P28 (Rescaling) (a) Divide each of the summary statistics by 12 so:
the mean is

22. P28 (Rescaling) (a) Divide each of the summary statistics by 12 so:
the mean is 4 feet
the standard deviation is

23. P28 (Rescaling) (a) Divide each of the summary statistics by 12 so:
the mean is 4 feet
the standard deviation is 0.2 foot
the median is

24. P28 (Rescaling) (a) Divide each of the summary statistics by 12 so:
the mean is 4 feet
the standard deviation is 0.2 foot
the median is 3.75 feet and
the IQR is

25. P28 (Rescaling) (a) Divide each of the summary statistics by 12 so:
the mean is 4 feet
the standard deviation is 0.2 foot
the median is 3.75 feet and
the IQR is 0.25 foot

26. P28
(b) each child growing 2 inches is ____________

27. P28 (Recentering)
(b) each child growing 2 inches is recentering

28. P28 (Recentering) (b) each child growing 2 inches is recentering
Which measures are affected by recentering?

29. P28 (Recentering) (b) each child growing 2 inches is recentering
Which measures are affected by recentering?
Only the centers:
mean
median

30. P28 (Recentering) (b) Add 2 to the measures of the center so
mean is 50 inches
median is 47 inches
Recentering does not change the spread so
standard deviation stays 2.4 inches
IQR stays 3 inches

31. P28 (Recentering and Rescaling)
(c) each child growing 4 inches is recentering and converting heights to feet is rescaling.

32. P28 (Recentering and Rescaling)

33. P28 (Recentering and Rescaling)

34. Plot this data into a stem-and-leaf plot:
23, 125, 8, 23, 50

35. Plot this data into a stem-and-leaf plot:
23, 125, 8, 23, 50
0 8
5 0
12 5

36. Plot this data into a stem-and-leaf plot:
23, 125, 8, 23, 50
0 8
5 0
12 5
5 0 represents 50

37. Page 69, P15

38. P15 The new mean height will be about 4 feet 4 inches.
x = [5(4) + 6]÷ 6

39. P15 The new mean height will be about 4 feet 4 inches.
The median will not change because it will
still be one of the heights of the 3rd graders,
who all are about 4 feet tall.

40. Page 70, P21 Use calculator to find (a) 5-number summary
and (e) to draw a modified boxplot.
Also answer (b), (c), and (d),

41. P21

42. P21

43. P21

44. Page 72, E33 Enter Predator data in List 1
Enter NonPredator data in List 2

45. Page 72, E33 Enter Predator data in List 1
Enter NonPredator data in List 2
Use L1 for Plot 1 and L2 for Plot 2 to display both modified boxplots on same screen

46. E33

47. Page 73, E43

48. Page 73, E43
Enter Weights in List 1
Enter Frequency in List 2

49. E43

50. Page 81, E53

51. Page 81, E53
Median: 23 or 24 cents.
To estimate this, find the amount of change that corresponds to the 50th percentile

52. Page 81, E53
Median: 23 or 24 cents.
To estimate this, find the amount of change that corresponds to the 50th percentile
b. Q1 ≈ 10 cents and Q3 ≈ 70 cents.
Q1 corresponds to 25th percentile and Q3 corresponds to 25th percentile
IQR = 60 cents

53. E53

54. Page 82, E54

55. E54

56. Page 82, E57

57. E57

58. Questions?