SOL A.9 Statistical Variation WS
Mr. Hannam
Name: ______________________________________________ Date: ______________ Block: _______
Statistical Variation – Worksheet
1) Evaluate each summation.
a)
5
3
 (i  1)
i 1
b)
i
i 1
5
n
c)
x
i 1
n
i
where n = 5 and x is an element of
{80, 98, 84, 95, 87}
2) Find the mean, mean absolute deviation (MAD), variance, and standard deviation by
hand for this data set: {1 3 5 7}
3) For each set of data below, find the mean, MAD, standard deviation, and variance. You
may use the graphing calculator. Round to the nearest hundredth if necessary.
a) {10, 7, 13, 10, 8}
b) {15, 17, 15, 17, 21, 17, 15, 23}
mean = _______ σ = __________
mean = _______ σ = __________
MAD = _______ σ2 = _________
MAD = _______ σ2 = _________
c) {40, 46, 41, 46, 49, 49, 46, 44, 44}
mean = _______ σ = __________
MAD = _______ σ2 = _________
d) {50.8, 51.6, 52.5, 52.8, 53.1}
mean = _______ σ = __________
MAD = _______ σ2 = _________
4) On six consecutive Sundays, a tow-truck operator received 9, 7, 11, 10, 13, and 7
service calls. Calculate the mean, MAD, and the standard deviation.
5) The following are the wind velocities reported at an airport at 6 p.m. on eight
consecutive days: 13, 8, 15, 11, 3, 10, 12, and 8 mph. Calculate the mean, MAD, and
standard deviation.
6) The mean length of Beethoven’s nine symphonies is 37 minutes; the
standard deviation is 12 minutes. How many standard deviations are
needed to include all the data values below, the times of the nine
symphonies?
27 min, 30 min, 47 min, 35 min, 30 min, 40 min, 35 min, 22 min, 65 min
7) What are the z-scores for each symphony in question 6 (round to the nearest
hundredth)?
8) A z-score for an element is 1.5 when the mean is 10 and the standard deviation is 5.
What is the value of the element?
SOL A.9 Statistical Variation WS
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9) Diane oversees production of ball bearings with a diameter of 0.5 inches at three
locations in the United States. She collects the standard deviations of a sample of ball
bearings each month from each location to compare and monitor production. The data
is shown below:
Compare and contrast the standard deviations from each plant location, looking for
trends and potential issues with production. What conclusions or questions might be
raised from the statistical data provided?
10) Jim needs to purchase a large number of 20-watt florescent light bulbs for his
company. He has narrowed his search to two companies offering the 20-watt bulbs for
the same price. The Bulb Emporium and Lights-R-Us both claim that their 20-watt
bulbs last for 10,000 hours. Which descriptive statistic might assist Jim in making the
best purchase? Explain.
11) In a school district, Mr. Mills is in charge of SAT testing. In a meeting, the
superintendent asks him how many students scored less than one standard deviation
below the mean on the mathematics portion of the SAT in 2009. He looks through his
papers and finds that the mean of the scores is 525 and 1653 students took the SAT in
2009. He also found a chart with percentages of z-scores on the SAT in 2009 as follows:
Use this information to help Mr. Mills find how many students scored less than one
standard deviation below the mean on the mathematics portion of the SAT. Explain how
you got your answer.