Statistics 101
Exam 1
February 13, 2002
Name:
ID#
INSTRUCTIONS: Read the questions carefully and completely. Answer each question and show work in
the space provided. Partial credit will not be given if work is not shown. When asked to explain, describe,
or comment, do so within the context of the problem.
1. [15 pts] The weight of 34 fish (Bream) caught in a lake near Tampere in Finland is given in the
stem-and-leaf plot below. The stem is 100s of grams and the leaf is 10s of grams. The weight 2|4 is
thus 240 grams.
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(a) [1] Does the stem-and-leaf plot use a split stem?
(b) [5] Calculate a five number summary for the 34 fish weights.
(c) [6] Use the following summaries to compute the mean and standard deviation of the fish weights.
X
X
n = 34
X = 20210
(X − X)2 = 971238.24
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(d) [3] Describe the shape of the histogram of fish weights.
2. [15 pts] Short Answer
(a) [3] The average of 10 numbers is 20. If one of those 10 numbers is changed from a 23 to a 43,
what is the new average?
(b) [3] For a set of 100 observations; the distance from the minimum to the lower quartile is 1.8, from
the lower quartile to the median is 0.9, from the median to the upper quartile is 0.4 and from the
upper quartile to the maximum is 0.1. Describe the shape of the distribution.
(c) [3] The median of 11 numbers is 20. If one of those 11 numbers is changed from 23 to 43, what
is the new median?
(d) [3] The least squares slope relating Y to X is 1.50. Additionally, X̄ = 10, Ȳ = 20, sX = 3.2 and
sY = 6.0. What is the value of the correlation coefficient, r, relating Y to X?
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(e) [3] In class we mentioned another measure of center, the midrange whose formula is given by
minimum + maximum
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What is the relationship between the median and the midrange for a distribution that is skewed
right?
3. [10 pts] Tenderness and flavor of pork is related to the pH of the meat. The higher the pH, the more
tender and flavorful. Swine are subjected to one of two different treatments and the pH of the meat is
examined. Below are box plots for the pH values.
(a) [5] Give the value of the range and the InterQuartile Range (IQR) for the Treatment 2 pH
measurements.
(b) [3] Describe the shape of the distribution of Treatment 2 pH measurements.
(c) [2] Will the mean pH be smaller than, approximately equal to, or larger than the median pH for
Treatment 2? Explain briefly.
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4. [35 pts] Diamonds are priced according to size (carats), color (D,E,F,G,H, or I) and clarity. Below is
a plot of the relationship between size (carats) and cost (Singapore $) for 44 diamonds with color code
E (a bright white color).
(a) [3] Describe the general relationship between size and cost.
(b) [5] Below are summaries of the size, X and the cost, Y.
n = 44,
X = 0.623,
Y = 5508,
sX = 0.268,
sY = 3605,
X
(X − X)(Y − Y ) = 40380.8
Compute the value of the correlation coefficient.
(c) [5] The slope of the least squares regression line relating cost, Y to size, X is 13075.0. Give an
interpretation of this value within the context of the problem.
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(d) [5] Compute the value of the intercept of the least squares regression line (round to one decimal
place) and give the equation for predicting cost from size.
(e) [3] Use the regression equation in (d) to predict the cost of a
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2
carat color E diamond.
(f) [3] Put the least squares regression line on the plot. It must be clear to me that you use the
regression equation from (d) to plot the line.
(g) [3] How much of the variability in cost is explained by the linear relationship with size?
(h) [5] Below is a plot of residuals versus size. Describe the pattern of the residuals and identify any
unusual residuals.
(i) [3] What does this plot of residuals tell you about how well the straight line fits the data?
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