1. Data Set: Apartment Rents (in ascending order)

2. Standardized Values for Apartment Rents

3. Sample Variance for Grouped Data
Example: Apartment Rents
continued

5. Classes
Frequency
Class Midpoint (M)
f*M
f*M2 2
102
204
20.808 8
107
856
91.592 18
112
2.016 13
117
1.521 7
122
854 1
127
16.129
132
17.424 50
5.710

6. A student scored 65 on statistics test that had a mean of 50 and a standard deviation of 10, she scored 30 on history test with a mean of 25 and a standard deviation of 5.
Compare her relative positions on the two tests

7. Test A: X=38 Sample Mean=40 St. Dev.=5 Test B: X=94 Sample Mean=100
Find z-scores for each test, and state which is higher.
Test A:
X=38
Sample Mean=40
St. Dev.=5
Test B:
X=94
Sample Mean=100
St. Dev.=10

8. A X=12 Sample Mean=10 St. Dev.=4 B X=170 Sample Mean=120 St. Dev.=32 C
Which score has the highest relative position. A
X=12
Sample Mean=10
St. Dev.=4 B
X=170
Sample Mean=120
St. Dev.=32 C
X=180
Sample Mean=60
St. Dev.=8

9. The mean price of houses in a certain neighborhood is 50,000 USD and standard deviation is 10,000 USD. Find the price range for which at least 75% of the houses will sell.

10. A survey of local companies found that the mean amount of travel allowances for executives was 0.25 USD per mile. The standard deviation was 0.02 USD. Using Chebyshev`s Theorem find the minimum percentage of the data values that will fall between 0.20 USD and 0.30 USD.

11. Example: Apartment Rents (TL)

12. Table: Ordered Array of Aptitude Test Scores for 40 Job Applicants.
∑x=2338 and ∑x2=157262
App.
Grade 1 20 11 42 21 56 31 78 2 12 43 22 58 32 80 3 23 13 59 33 81 4 25 14 46 24 61 34 85 5 30 15 48 62 35 90 6 16 50 26 65 36 92 7 17 51 27 68 37 96 8 39 18 52 28 70 38 98 9 40 19 54 29 71 99 10 41 55 75
100

13. Why do we need the standard deviation?
1- The standard deviation reflects dispersion of data values, so that the dispersion of different distributions may be compared by using standard deviations.
2- The standard deviation permits the precise interpretation of data values within a distributions.
3- The standard deviation, like the mean, is a member od a mathematical system which permits its use in more advanced statistical considerations.

14. EMPIRICAL RULES
1- About 68% of the values will lie within 1 standard deviation of the mean, that is, between x̄ - s and x̄ + s;
2- About 95% of the values will lie within 2 standard deviation of the mean, that is, between x̄ - 2s and x̄ + 2s;
3- About 99.7% of the values will lie within 3 standard deviation of the mean, that is, between x̄ - 3s and x̄ + 3s;

15. Problem
Based on a survey of dental practitioners, the study reported that the mean number of units of local anesthetics used per week by dentists was 79, with a standard deviation of 23. Suppose we want to determine the percentage of dentists who use less than 102 units of local anesthetics per week.
a- Assuming nothing is known about the shape of the distribution for the data, what percentage of dentists use less than 102 units of local anesthetics per week?
b- Assuming that the data has a mound-shaped (bell-shaped or symmetric) distribution, what percentage of dentists use less than 102 units of local anesthetics per week?

16. Mean Standard Deviation Hand rubbing 35 59 Hand washing 69 106 Problem
Based on the study to compare the effectiveness of washing the hands with soap and rubbing the hands with alcohol-based antiseptics.
Table: Descriptive statistics on bacteria counts for the two groups
of health care workers.
Mean
Standard Deviation
Hand rubbing 35 59
Hand washing 69
106
a- For hand rubbers, form an interval that contains at least 75% of the bacterial counts.
b- For hand washers, form an interval that contains at least 75% of the bacterial counts.
(Note that the bacterial count cannot be less than 0)
c- On the basis of your results in parts a and b, make an inference about the effectiveness of the two hand cleaning methods.