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Measures of Center and Spread

Total questions: 16

Worksheet time: 2hrs 30mins

Name
Class
Date
1.
What is the standard deviation for the data given:
{12, 13, 29, 18, 61, 35, 21}
a)
293.67
b)
15.87
c)
17.14
d)
41.98
2.

If the data set is approximately normal, what percent of people are within 1 standard deviation of the mean?

a)

99.7

b)

34

c)

68

d)

95

3.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?
a)
68%
b)
99.7%
c)
95%
d)
84%
4.
Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
5.
Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3? 
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
6.
How can we tell who "did better" between someone who got a 31 on the ACT and someone who got 1400 on the SAT?
a)
Random guess?
b)
1400 is higher so it's better
c)
Find the Z-scores!
d)
Flip a coin?
7.
Adam's Z-score on a test is +2.5.  What does this mean?
a)
He'd better start studying.
b)
He did better than EVERYONE.
c)
He scored 2.5 standard deviations above the average.
d)
He did terrible.
8.

If Gonzalo's score is 87, the class average is 82, and the SD is 4, how many standard deviations is he above the mean?

a)

-1.25

b)

+1.25

c)

+1.20

d)

+1.02

9.
The average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  
a)
2
b)
1
c)
-2
d)
-1
10.
The mean age of sales people in ABC Dept. Store is 30 years with a standard deviation of 6 years.  Between which two age limits must at least 75% of the data lie?
a)
24 - 36 years
b)
18 - 42 years
c)
12 - 48 years
d)
6 - 54 years
11.

The mean score in an accounting test is 80 with a standard deviation of 10. Between which two scores must the mean lie to represent at least 89% of the data set?

a)

70 - 90

b)

60 - 100

c)

50 - 110

d)

40 - 120

12.

The mean age of a dinosaur fossil in a particular fossil bed is 85 million years. The standard deviation of the fossil ages from this bed is 2.5 million years. At least __________ of fossils in this bed are between 80 and 90 million years old.

a)

75 %

b)

89 %

c)

2%

d)

70%

13.
The data set below has an outlier of 42.
2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42
What effect does removing the outlier have on the distribution of the data?
a)
The mean will decrease
b)
The median will decrease
c)
The mean will increase
d)
The median will increase
14.
The hourly salaries of the workers at a restaurant are shown below.
$7.75, $8.50, $7.25, $9.00, $30.00, $8.25, $7.75, $9.00
Which statement is true?
a)
The worker who earns $7.25 an hour causes the mean to be a better representation of the typical salary than the median.
b)
The worker who earns $7.25 an hour causes the median to be  a better representation of typical salary than the mean.
c)
The worker who earns $30.00 an hour causes the mean to be a better representation of the typical salary than the median.
d)
The worker who earns $30.00 an hour causes the median to be a better representation of the typical salary than the mean.
15.

The distribution of data is skewed right. What is the relationship between the mean and median?

a)

median > mean

b)

mean > median

c)

mean = median

d)

Impossible to tell.

16.

Which of the following is NOT affected by outliers?

a)

mean

b)

standard deviation

c)

IQR

d)

range