Download Statistics Review Answers

Accelerated Math 2
Statistics Review
1. The salaries at a small business with 6 employees are as follows: $255,000, $32,000, $28,000,
$24,000, $22,000, and $22,000. Find the mean, median, and mode of the salaries, explain which
measures best represent a typical employee’s salary, and the reason why.
Median would represent
best because of the outlier.
Mean = $ 63,833.33 Median = $ 26,000 Mode = $ 22,000
2. Given the following set of data, find the following measures of central tendency and spread. Then add
6 to each measurement and recalculate the measures of central tendency and spread of the revised
measurements. How are the measures of central tendency changed? The measures of spread?
5, 12, 7, 14, 8, 9, 7
Mean________
8.9
Median_______
8
7
Mode________
_______
2.9
IQR______
5
Mean_________
14.9
Median_______
14
The measures of spread
all remained the same
_______
2.9
but all the measures of
IQR ______ central tendencies went
5
up by 6.
Mode_________
13
3. Given the following set of test scores create a line plot for the set of data, find the mean and standard
deviation. Then determine if the following data can be considered a normal distribution.
66, 75, 74, 78, 88, 99, 75, 88, 76, 74, 66, 89, 82, 92, 67, 89, 88, 84, 92, 65, 75, 85, 78, 79, 84, 94,
91, 81, 61, 79
70% within 1 , but 100% of
the data within 2 . So this
is probably not a normal
distribution.
Mean ________
80.5
________
9.5
4. Ms. Gray’s 46 students had a mean score of 87 on the last test. Mr. Lamb’s 26 students had a mean
46 (87)+ 26 (91)
score of 91. Find the mean score of all 72 students.
5. Make a frequency table and a histogram for the data set.
72
= 88.4
0.2, 1.3, 5.4, 4.3, 2.2, 4.3, 4.6, 3.5, 5.2, 4.8, 1.5, 3.7, 5.4, 4.0, 4.3, 5.2, 3.1, 2.9, 4.6, 4.8
Frequency Table
Value Frequency
0-1
1-2
2-3
3-4
4-5
5-6
1
2
2
3
4
2
6. Create a box-and-whisker plot for the data set.
42, 45, 56, 48, 59, 60, 51, 54, 44, 51, 50, 44, 42, 49, 56
45
40
50
55
60
7. The table below lists the number of customers for a fast-food restaurant. Find the range and the
standard deviation for the data.
= 633.02
Range = 2167
12375
11982
12025
13890
12098
12502
13202
11829
12654
12825
13234
11723
8. Given a data set comprised of 5144 measurements that is bell shaped with a mean of 868. If 95%
percent of the data lies between 854, and 882 then what is the standard deviation?
868 + 2
= 882 or 868 – 2
= 854
So, = 7
9. Given a group of data with mean 50 and standard deviation 6, at least what percent of the data will fall
50 + a(6) = 68 or 50 – a(6) = 32
between 32 and 68?
a = 3 in either case
So, the % of the data within 3
is 99.7%
10. A z-score is: It is a way of comparing two unlike quantities by their relation to the mean. This is
accomplished by scaling the distribution so the mean is 0 and each
is worth 1.
11. If a group of data has a mean of 80 and a standard deviation of 13.6, what is the raw score interval that
should contain the lower 75% of the data?
x - 80
x - 80
-3.9 =
and 0.7 =
13.6
13.6
x = 26.96 and x = 89.52
12. Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is
increased by 25, what are the new mean and standard deviation?
Mean = 525
= 100
13. In a certain southwestern city the air pollution index averages 62.5 during the year with a standard
deviation of 18.0. Assuming that the empirical rule is appropriate, the index falls within what interval
95% (over the middle) of the time?
62.5 + 2(18) and 62.5 – 2(18)
26.5 and 98.5
14. The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What
is the z-score of Windex with a cost of 10.1 cents per ounce?
0.96 =
10.1- 7.7
2.5