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M116 - Elements of Statistics – Reviewing chapters 1-3
1. Use the given sample data to find each of the listed values. Show your work.
52 69 85
a)
x
2
b)
c) Find the mean
( x ) 2
d) Find the standard deviation
2. Use the given sample data to answer the questions given below. Show your work
whenever appropriate.
74 88 76 72 87 73 81 86 79 76
a) Construct a dot plot for the data.
b) Find Q1
c) D7
d) Find the median of the data.
e) Find the mode of the data.
f) Find the range of the data.
g) Find the midrange of the data
h) Find the percentile corresponding to 73
3. Fifteen workers were asked about their ages. The data is found below.
26
21
39
41
46
41
52
39
27
51
43
38
41
33
26
a) Construct an ordered stem-and-leaf plot for the data with the stem defined to be the
tens digit.
b) Construct and label a box plot of the data. You can use your calculator for this one.
Please transfer a NEAT graph to this paper.
List the 5-number summary.
c) Construct a frequency table with 4 classes using the smallest number as the lower
limit of the first class. Show how you find the class width.
d) Find the relative frequencies, midpoints, cumulative frequencies, class boundaries.
e) Use the calculator to find the mean and standard deviation of the raw data
f) Use the calculator to find the mean and standard deviation of the grouped data
g) Compare the results to (e) and (f) and comment.
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4. Suppose you are given 10 measurements: 5, 5, 5, 5, 6, 6, 6, 7, 7, 8
If you discovered that the data was incorrect because the largest observation was wrong:
instead of 8, it should be 18. Which of the following are not affected? _______
a) the median b) the mean c) the standard deviation d) the range
5. If IQ scores of a group of students have a mean of 110 and a standard deviation of
12,
a) What can you conclude from Chebyshev's theorem about the percentage of IQ scores
between 86 and 134?
b) If we assume the distribution is normal we can use the ________________ rule.
Using this rule, complete each of the following:
(1) _____________% of the students have z scores between 98 and 122.
(2) 99.7 % of the students have z scores between ______ and ____________
(3) We consider unusual IQ score below _______ and above __________
6.
a) Create a list of 7 numbers with standard deviation 0.
b) Create a list of 5 different numbers with a median of 10.
c) Create a list of 4 different numbers with a median of 10.
d) Create a list of of 10 numbers which is bimodal.
e) Create a list of 4 different numbers with a mean of 10.
f) Create a list of 8 numbers with a range of 10.
g) Create a list of 6 numbers with a midrange of 10.
7. Identify the following as either continuous or discrete:
a) The average weight of all freshmen entering college in a certain year is 134.5 pounds.
b) The number of high school graduates for a certain school in a certain year is 321.
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8. For each of the following measurements associated with student life, determine which
of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate:
a) Length of time to complete an exam.___________________________
b) Year in which we were born.
___________________________
c) Social security numbers.____________________________
d) Course evaluation scale: poor, acceptable, good. ____________________________
e) Score on last exam (based on 100 possible points).___________________________
9. For each of the following examples of sampling students from Montgomery College,
identify the type of sampling (random, convenience, stratified, systematic or cluster)
a) A study is done by selecting randomly 35 in-state students and 35 out-of-state
students._______________
b) A pollster writes the names of each student on a card, shuffles the cards, then
draws 25 names._________
c) A study is done by interviewing every eighth student going through the cafeteria
line at lunch __________
d) A pollster selects everyone in each of 10 randomly selected
classrooms.______________________
e) A study is done by interviewing the first 50 students coming into the library.
_____________________
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