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Abraham Baldwin Agricultural College
MATH 2000, PRACTICE TEST 1
Name:____________________________
1. For 100 employees of a large department store, the following distribution for years of
service was obtained. Construct a frequency distribution, histogram, frequency polygon and
ogive for the data. Make sure you label the axes.
Class limits
15
610
1115
1620
2125
2630
Histogram:
Frequency polygon:
Frequency
20
25
35
5
10
5
Ogive:
2. Using the chart for question number 1, find the mean, variance, and standard deviation.
3. Construct a frequency distribution with four classes for the following data:
22, 38, 11, 40, 10, 32, 26, 12, 47, 39, 28, 40, 17, 34.
Make it clear how you determine the classes.
4. Create a stem and leaf plot for the data in number 3.
5. Find the mean, median and midrange for the following set of data.
61, 11, 1, 3, 2, 30, 18, 3, 7, 8
6. Find the range, variance and standard deviation for the following sample
2, 6, 5, 4, 0, 5
7. A sample of hourly wages of employees who work in restaurants in a large city has a mean
of $5.02 and a standard deviation of $0.09. Using Chebyshev’s Theorem, find the range in
which at least 75% of the data will lie.
8. Use the data given for question 2 to find the value representing the 30th percentile. Then
find the percentile rank for the number 32.
9. A math test has a mean score of 83 and a standard deviation of 5. Find the z-scores for the
following test grades: a. 91
b. 82
10. Construct a box plot for the following set of data.
11. Test the following data for potential outliers.
28, 8, 0, 31, 41, 2, 35, 5, 12, 50
3, 2, 7, 12, 15, 18, 21, 25, 27, 40, 74
Abraham Baldwin Agricultural College
MATH 2000, PRACTICE TEST 1 ANSWERS
1.
Class
limits
1-5
Class
boundaries
0.5-5.5
f
xm
cf
fxm
fxm2
20
3
20
60
180
6-10
5.5-10.5
25
8
45
200
1600
11-15
10.5-15.5
35
13
80
455
5915
16-20
15.5-20.5
5
18
85
90
1620
21-25
20.5-25.5
10
23
95
230
5290
26-30
25.5-30.5
5
28
100
140
3920
1175
18525
SUMS
100
 fx
1175
 11.75  11.8 round to one decimal place since the data is in
n
100
whole numbers – we assume this because the classes are given as whole numbers;
2.
x 
s2 
s 
3.
m
n fxm2 

  fx 
2
m
n  n  1
n fxm2 
  fx 
n  n  1
Class limits
10 20
21  31
32  42
43  53
m
100*18525  1175
 47.6641  47.7 ;
100*99
2

2
 6.90392  6.9
Frequency
4
3
6
1
4.
stem
1
2
3
4
5.
x  14.4 ; Median = 7.5, MR = 31
6.
range = 11; variance = 16.4; and standard deviation = 4.05
leaf
0127
268
2489
007
7. At least 75% of the data will be in the interval $4.84 to $5.20; k = 2. Use the formula
x  ks to find the boundaries
np
14*30
8. The value representing the 30th percentile is c 

 4.2  5 Always
100
100
round up. Put the data in ascending order 10, 11, 12, 17, 22, 26, 28, 32, 34, 38, 39, 40, 40, 47
and the 5th data value is 22. The percentile rank for the number 32 is
# of data values below 32  .5
7.5

 .5357  54th percentile.
n
14
9. A math test has a mean score of 83 and a standard deviation of 5. Find the z-scores for the
following test grades: a. 91
b. 82
a. z 
xx
91  83

 1.6
s
5
b. z 
xx
82  83

 0.2
s
5
10. Construct a box plot for the following set of data.
28, 8, 0, 31, 41, 2, 35, 5, 12, 50
Put the data in ascending order
0, 2, 5, 8, 12, 28, 31, 35, 41, 50
You need to find the quartiles. The second quartile, Q2 , is the median.
12  28
Q2 
 20
2
The first quartile, Q1 , is the median of the data to the left of the position of the median. The
median is between 12 and 28 so there are five values, 0, 2, 5, 8, 12, to the left of the position of
Q1  5
median.
The third quartile, Q3 , is the median of the data to the right of the position of the median. The
median is between 12 and 28 so there are five values, 28, 31, 35, 41, 50, to the right of the
position of median.
Q3  35
Put vertical bars above the quartiles and draw a box around them. The draw lines extending to
the smallest value and largest value like so:
0
5
10
15
20
25
30
35
40
45
11. Test the following data for potential outliers.
3, 2, 7, 12, 15, 18, 21, 25, 27, 40, 74
50
55
The second quartile, Q2 , is the median. Q2  18
The first quartile, Q1 , is the median of the data to the left of the position of the median. The
median is at 28 so there are five values, 3, 2, 7, 12, 15, to the left of the position of median.
Q1  7
The third quartile, Q3 , is the median of the data to the right of the position of the median. The
median is at 28 so there are five values, 21, 25, 27, 40, 74, to the right of the position of
median.
Q3  27
The interquartile range is IQR  Q3  Q1  27  7  20
Values greater than Q1  1.5IQR or less than Q1  1.5IQR are potential outliers
Q1  1.5IQR  7  1.5(20)  23 and Q3  1.5IQR  27  1.5(20)  57
74 is a potential outlier.