practice- answers

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NAME: _________________________________
Describe each distribution (shape, center, spread):
1)
mean = 0.2
std dev =0.677
Median = 0
Q1 = -0.7
Q3 = 0.9
min = -1.8
max = 2.4
2)
mean = 1982
std dev = 25
Median = 1995
Q1 = 1985
Q3 = 2001
min = 1950
max = 2009
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



Unimodal, roughly symmetric
Center at mean of 0.2 units
Std deviation of 0.677 units
Range of (-1.8, 2.4) units
No outliers






Unimodal, left skewed
Center at median of 1995 years
IQR of 16 years
Range of (1950, 2009) years
No outliers
Gap at approx. 1955 years
3)
mean = 2.9
std dev = 0.3
Median = 3.35
Q1 = 2.7
Q3 = 3.6
min = 1.6
max = 4.5





Bimodal, left skewed
Center at median of 3.35 points
IQR of 0.9 points
Range of (1.6, 4.5) points
possible outlier at 4.5 points





Unimodal, slight left skew
Center at median of 5 units
IQR of 4.5 units
Range of (0,16) units
outlier at 16 units
4)
mean = 7.2
std dev = 2.7
Median = 5
Q1 = 3
Q3 = 7.5
min = 0
max = 16
5) Go back to the picture/summary stats in #4. Check to see if the highest observation is an outlier.
LF = 3 – (1.5 * 4.5) = -3.75
UF = 7.5 + (1.5 * 4.5) = 14.25
Normal data = (-3.75, 14.25)
Yes, the observation at 16 is an outlier
6) Using the following summary statistics, how many outliers are there?
min
2
a.
b.
c.
d.
e.
Q1
18
Med
22
Q3
25
Max
40
Work:
LF = 18 – (1.5*7) = 7.5
UF = 25 + (1.5*7) = 35.5
Normal data = (7.5, 35.5)
 Min (2) is an outlier
 Max (40) is an outlier
None
1
2
At least 1
At least 2
7) Create a frequency histogram of the list AGEMO. This is a list of the ages in months of the students in our
class.
13
10
8
#
6
3
190
200
210
220
Ages of students in months
8) Create a relative frequency histogram of the list PRES. These are the ages of death of all US presidents. Then
describe the distribution.
18.9
%
16.2
5.4
2.7
45
50
55
60
65
75
85
Presidents Ages of Death
95
Description: Right skewed, unimodal. Center at the Median of 67 years. Spread is an IQR of 18 years, and a
range of (46, 93) years.
9) Use the list HT (heights of students in our class)
a. Find the Mean, Median, Range, Q1, Q3, IQR, and Standard deviation.
mean
67.865
std dev
4.178
min
58
Q1
66
Med
68
Q3
71
Max
76
Range
(58, 76)
IQR
5
b. Create a boxplot of the data
-------------------------------------------------------------------58 59
66 68
71
76
Heights of students in our class
c. Suppose we add the data point 78” to this set of data. Indicate how each of the statistics in part (a) would
change: increase, decrease, or stay about the same.
mean
std dev
Increase Increase
min
Same
Q1
Same
Med
Same
Q3
Same
Max
Range
Increase Increase
IQR
Same
d. Going back to the original set of data: suppose we add the data point 50” to this set of data. Indicate how
each of the statistics in part (a) would change: increase, decrease, or stay about the same.
mean
std dev
min
decrease Increase decrease
Q1
Same
Med
Same
Q3
Same
Max
Same
Range
Increase
IQR
Same
10) Give a set of numbers that have a standard deviation of 0.
5, 5, 5, 5, 5, 5, 5
(any set of numbers where they are all the same)
11) Create parallel boxplots of the lists TST1F and TST1M. These are test scores for females and males.
FEMALES
MALES
----------------------------------------------------------------------------------20
45
55 62 68 76 82 90 92
TEST SCORES
12) Based solely on the mean and median given, decide on the shape of the distribution, and what measure of
center and spread you would report.
(a) Mean = 100
(b) Mean = 20
(c) Mean = 934
Median = 98
Median = 41
Median = 850
Approx. symm.
Mean & std dev.
Left skew
Median & IQR
right skew
median & IQR
13) The following are quiz scores from two Algebra 1 Classes.
Class 1: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82} and
Class 2: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
a. Find the means of both classes. Which would you rather be in?
Mean of Class 1 = 79.167
Mean of Class 2 = 78.667
I would rather be in Class 1- they have the higher mean
b. Find the standard deviations of both classes. Which class was more consistent in their scores? Why?
Std. Dev. of Class 1 = 13.361
Std. Dev. of Class 2 = 9.188
Class 2 had the more consistent scores. I would now rather be in class 2 because their mean was not
that much lower and they were more consistent. Class 1 was more spread out.
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