NAME: __________________________________________________________________________
Upward Bound Statistics Summer 2014
Posttest Review
Answer each question to the best of your ability. If you do not understand any
question, please seek assistance! These questions are very similar to those you will
see on your posttest.
77
83
21
81
93
85
41
91
94
90
100
95
64
72
70
1. Given the data above, find a) the mean, b) the median, c) the mode, d) the range, e) the
midrange, f) the sample standard deviation and g) the sample variance.
a.
b.
c.
d.
e.
f.
g.
Mean: 77.13
Median: 83
Mode: N/A
Range: 79
Midrange: 60.5
Sample standard deviation: 21.64
Sample variance: 468.12
2. Of the measures a-f above, which are measures of center? Which are measures of variation?
Mean, Median, Mode, and Midrange are measures of center. Range, standard
deviation, and variance are measures of variation.
3. Think back to the assignment where you had to calculate a standard deviation problem with
Microsoft Excel using columns A-D and creating a table. Of the following Excel formulas,
which would you need to actually get to the standard deviation and not just ∑(𝑥𝑖 − ̅̅̅
𝑥)? The
available options are AVERAGE, MEDIAN, SUM, SQRT, MIN, MAX, ^2, +, –. Is there another
way to find standard deviation and variance with Excel?
You need all of these Excel formulas except MIN and MAX. The other way to find
standard deviation and variance is to use the respective formulas STDEV.S and VAR.S.
4. What does an individual frequency distribution display in each column? A relative frequency
distribution? A cumulative frequency distribution?
An individual frequency distribution has the intervals of given data in one
column and individual counts of data points that fall into those intervals in the
other column. A cumulative frequency distribution has ascending “less than”
statements instead of intervals in the first column and a cumulative count of
data points in the second column.
5. Give three examples of each of the four levels of measurement: interval, ratio, ordinal,
nominal.
Interval: Temperature; dates when measures from an arbitrary or unclear
starting point (something AD); direction when measured in degrees from
magnetic north
6. What is the Empirical Rule? What is Chebyshev’s Theorem? What is the difference?
The Empirical Rule states that for a given bell-shaped distribution of data, 68% of the
data will fall within one standard deviation of the mean; 95% of the data will fall
within 2 standard deviations of the mean; and 99.7% of the data will fall within three
standard deviations of the mean.
7. Does all the data fall within 4 standard deviations of the mean on a bell-shaped curve?
No – in fact you can never reach a number of standard deviations that represents all
the data, because there will always be data points in the natural world that are
extreme and rare cases. You can say “arbitrarily close to all the data” though.
8. A piece of swimwear that costs $30 is marked down 25% for a sale. At the end of the sale, it
is marked up 20%. How much does this piece of swimwear cost after the sale?
$30 – (30 * .25) = $22.50
$22.50 + ($22.50 * .20) = $27.00
9. What are four ways in which statistics collected from surveys can be unreliable?
Bad (or misleading) use of percentages
Voluntary Response Sample
Small-n studies
Bad pictographs (pictures that are intended to communicate numerical values)
Bad graphs
Self-interest studies
Partial pictures
10. Find the following probabilities:
a. The probability of a person being born in February or March 59/365 = .162
b. The probability of a person being born on a day that ends in the letter y 1.00
c. The probability of picking a red card out of a standard deck of playing cards given that
the suit is hearts 1.00
d. The probability of picking a jack out of a standard deck of playing cards 4/52 = .0769
e. The probability of picking a card whose suit is spades out of a standard deck of playing
cards 13/52 = 0.250
f. The probability of picking a state beginning with the letter A out of a hat containing
all 50 states written on slips of paper 4/50 = .0800
11. Complete all the even problems on Probability Intensive Worksheet #2.
See worksheet solutions for solutions to these problems.
12. Complete all the even problems on Probability Intensive Worksheet #3.
See worksheet solutions for solutions to these problems.
13. In probability, what does replacement mean? Use marbles in a 2-3 sentence written example
of the difference between probability with replacement and probability without replacement.
Replacement means “putting back an item drawn out of a collection of items
before drawing the next item.” For example, you have 20 marbles in a bag, 10
green and 10 blue. The probability of pulling a green marble is 10/20 or ½. If
you put back that green marble, the probability of pulling blue in the next draw
is also 10/20. But if you do not replace that marble, the probability of the
second event, drawing blue, will be 10/19 because only 19 marbles are left in
the bag.
14. A probability of 0 means what about the event? A probability of 1 means what about the
event?
0 is used for impossible events; 1 is used for certain events.
Given the crosstabulation below, answer the following questions.
P5d. Does R have a gun in his or her home or garage? * X1. Ever attend
church/religious services? Crosstabulation
Count
P5d. Does R have a gun in his
or her home or garage?
Total
1. Yes
5. No
X1. Ever attend church/religious
services?
1. Yes
5. No
295
129
493
265
788
394
Total
424
758
1182
15. What is the probability that a randomly chosen respondent has a gun in his or her home or
garage?
16. What is the probability that a randomly chosen respondent does not attend religious
services?
17. What is the probability that a randomly chosen respondent has a gun in his or her home or
attends religious services?
18. What is the probability that a randomly chosen respondent has a gun in his or her home or
does not attend religious services?
19. What is the probability that a randomly chosen respondent attends religious services given
that he or she does not own a gun?
20. What is the probability that a randomly chosen respondent owns a gun given that he or she
does not attend religious services?