1. Section 3:3 Answers page 164-5 #4-14 even
Class
Midpoint (xi)
Frequency (fi)
(xi)* (fi)
((xi)-(x))2* (fi)
0-499
250 5
1250
750 17
12750 36
45000
1750
121
211750
2250
119
267750
2750 81
222750
3250 47
152750
3750 45
168750
4250 22
93500
4750 7
33250
Sum
500
Mean
2419
Sample Variance
Standard Dev.

2. Section 3:3 Answers page 164-5 #4-14 even
Class
Midpoint (xi)
Frequency (fi)
(xi)* (fi)
((xi)-(x))2* (fi)
0-17 9
12827
115443
18-24
21.5
5047
25-34 30
4920
147600
35-44 40
4049
161960
45-54 50
3399
169950
55-59
57.5
1468
84410
60-64
62.5
1357
65+ 70
3394
237580
Sum
36461
Mean
Sample Variance
Standard Dev.

3. Section 3:3 Answers page 164-5 #4-14 even
Class
Midpoint (xi)
Frequency (fi)
(xi)* (fi)
((xi)-(x))2* (fi)
225
13159
275
23083
325
59672
375
124616
425
202883
475
243569
525
247435
575
213880
625
156057
675
120933
725
54108
775
35136
Sum
Mean
Sample Variance
Standard Dev.

4. Section 3:3 Answers page 164-5 #4-14 even
c. By the Empirical rule, 95% of the data lie within 2 standard deviation of the mean so 95% of the SAT Math scores are between and 748.1

5. Section 3:3 Answers page 164-5 #4-14 even

6. Objective(s) To approximate the mean of a variable from grouped data.
To compute the weighted mean.
To approximate the variance and standard deviation of a variable from grouped data
Check off on your MATRIX

7. Chapter 3 Numerically Summarizing Data
3.4
Measures of Location

8. Objective(s) To determine and interpret z-scores
To interpret percentiles
To determine and interpret quartiles
To determine and interpret the interquartile range
To check a set of data for outliers

9. Warm-up Type 1 Writing / 3 lines or more – 2 minutes
What does the word “quartile” mean?
What do you think the word “percentile” means?

10. The z-score represents the number of standard deviations that a data value is from the mean.
It is obtained by subtracting the mean from the data value and dividing this result by the standard deviation.
The z-score is unitless with a mean of 0 and a standard deviation of 1.

11. Population Z - score
Sample Z - score

12. EXAMPLE Using Z-Scores
The mean height of males 20 years or older is 69.1 inches with a standard deviation of 2.8 inches. The mean height of females 20 years or older is 63.7 inches with a standard deviation of 2.7 inches. Data based on information obtained from National Health and Examination Survey. Who is relatively taller:
Shaquille O’Neal whose height is 85 inches or
Lisa Leslie whose height is 77 inches.

13. The median divides the lower 50% of a set of data from the upper 50% of a set of data. In general, the kth percentile, denoted Pk , of a set of data divides the lower k% of a data set from the upper (100 – k) % of a data set.

14. Computing the kth Percentile, Pk
Step 1: Arrange the data in ascending order.

15. Computing the kth Percentile, Pk
Step 1: Arrange the data in ascending order.
Step 2: Compute an index i using the following formula:
where k is the percentile of the data value and n is the number of individuals in the data set.

16. Computing the kth Percentile, Pk
Step 1: Arrange the data in ascending order.
Step 2: Compute an index i using the following formula:
where k is the percentile of the data value and n is the number of individuals in the data set.
Step 3: (a) If i is not an integer, round up to the next highest integer. Locate the ith value of the data set written in ascending order. This number represents the kth percentile.
(b) If i is an integer, the kth percentile is the arithmetic mean of the ith and (i + 1)st data value.

17. EXAMPLE Finding a Percentile
For the employment ratio data on the next slide, find the
(a) 60th percentile
(b) 33rd percentile

20. Finding the Percentile that Corresponds to a Data Value
Step 1: Arrange the data in ascending order.

21. Finding the Percentile that Corresponds to a Data Value
Step 1: Arrange the data in ascending order.
Step 2: Use the following formula to determine the percentile of the score, x:
Percentile of x =
Round this number to the nearest integer.

22. EXAMPLE Finding the Percentile Rank of a Data Value
Find the percentile rank of the employment ratio of Michigan.

23. The most common percentiles are quartiles
The most common percentiles are quartiles. Quartiles divide data sets into fourths or four equal parts.
The 1st quartile, denoted Q1, divides the bottom 25% the data from the top 75%. Therefore, the 1st quartile is equivalent to the 25th percentile.

24. The most common percentiles are quartiles
The most common percentiles are quartiles. Quartiles divide data sets into fourths or four equal parts.
The 1st quartile, denoted Q1, divides the bottom 25% the data from the top 75%. Therefore, the 1st quartile is equivalent to the 25th percentile.
The 2nd quartile divides the bottom 50% of the data from the top 50% of the data, so that the 2nd quartile is equivalent to the 50th percentile, which is equivalent to the median.

25. The most common percentiles are quartiles
The most common percentiles are quartiles. Quartiles divide data sets into fourths or four equal parts.
The 1st quartile, denoted Q1, divides the bottom 25% the data from the top 75%. Therefore, the 1st quartile is equivalent to the 25th percentile.
The 2nd quartile divides the bottom 50% of the data from the top 50% of the data, so that the 2nd quartile is equivalent to the 50th percentile, which is equivalent to the median.
The 3rd quartile divides the bottom 75% of the data from the top 25% of the data, so that the 3rd quartile is equivalent to the 75th percentile.

26. EXAMPLE Finding the Quartiles
Find the quartiles corresponding to the employment ratio data.

27. Checking for Outliers Using Quartiles
Step 1: Determine the first and third quartiles of the data.

28. Checking for Outliers Using Quartiles
Step 1: Determine the first and third quartiles of the data.
Step 2: Compute the interquartile range. The interquartile range or IQR is the difference between the third and first quartile. That is,
IQR = Q3 - Q1

29. Checking for Outliers Using Quartiles
Step 1: Determine the first and third quartiles of the data.
Step 2: Compute the interquartile range. The interquartile range or IQR is the difference between the third and first quartile. That is,
IQR = Q3 - Q1
Step 3: Compute the fences that serve as cut-off points for outliers.
Lower Fence = Q (IQR)
Upper Fence = Q (IQR)

30. Checking for Outliers Using Quartiles
Step 1: Determine the first and third quartiles of the data.
Step 2: Compute the interquartile range. The interquartile range or IQR is the difference between the third and first quartile. That is,
IQR = Q3 - Q1
Step 3: Compute the fences that serve as cut-off points for outliers.
Lower Fence = Q (IQR)
Upper Fence = Q (IQR)
Step 4: If a data value is less than the lower fence or greater than the upper fence, then it is considered an outlier.

31. EXAMPLE Checking for Outliers
Check the employment ratio data for outliers.

32. West Virginia

33. Objective(s) To determine and interpret z-scores
To interpret percentiles
To determine and interpret quartiles
To determine and interpret the interquartile range
To check a set of data for outliers