STAT 1000-022. Introduction to tatistics
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STAT 1000-022. Introduction to tatistics, May 2022
Practice Examples: Ch. 1-3 Lecture Slides
1. The following sample data are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity.
25, 27, 31, 33, 26, 28, 38, 40, 24, 32, 35, 40
(a) Calculate the range.
(b) If we want to construct a histogram with 4 classes, what should the width of the classes be?
(c) Calculate the mean and the median.
(d) Based on the values in (c), what can we say about the shape of the distribution of the sample?
(e) Construct a stem-and-leaf plot.
2. Are the following variables qualitative (categorical) or quantitative (numerical)?
(a) The number of credits a student has earned.
(b) The departments at a university.
(c) Income tax brackets in dollars (e.g. Below 8925, 8925-36250, 36250-87850, etc.).
(d) The number of points scored per game by a UConn basketball player.
3. Assume a sample of interest has a bell-shaped distribution with a sample mean of 100 (i.e. 
= 100) and a sample standard deviation of 12 (i.e. s = 12). Answer the following questions based on the empirical rule.
(a) Construct intervals for each of the following:
(i) An interval containing points 1 standard deviation away from the mean, i.e., [
− 1s,
+ 1s].
(ii) An interval containing points 2 standard deviation away from the mean, .e., [
− 2s,
+ 2s].
(iii) An interval containing points 3 standard deviation away from the mean, i.e., [
− 3s, 
+ 3s].
(b) Answer the following questions regarding the corresponding intervals in 1a).
(i) Approximately what percentage of the sample measurements (observations) can be approx- imated by the interval in (i) above? That is, approximately what percentage of sample measurements do we expect to be contained in this interval?
(ii) Approximately what percentage of the sample measurements (observations) can be approxi- mated by the interval in (ii) above?
(iii) Approximately what percentage of the sample measurements (observations) can be approxi- mated by the interval in (iii) above?
(c) Approximately what percentage of sample measurements do we expect to be within the following values?
(i) 76 and 100
(ii) 88 and 124
(iii) 64 and 76
4. Data on different types of flat fish are shown below.
|
Flounder Flounder Turbot Turbot |
Halibut Turbot Turbot Sole |
Turbot Flounder Halibut Halibut |
Turbot Sole Sole Sole |
Flounder Sole Flounder Flounder |
(a) Construct a (relative) frequency table and a bar chart. (Hint: see the faculty rank data example in the Ch. 1 lecture slides.)
Construct a bar chart.
5. The following are grade point averages measured in a sample of 8 undergraduate students who are applying to graduate schools in public health.
3.28, 2.97, 2.05, 3.61, 3.95, 2.95, 3.00, 3.10
(a) What is the sample size?
(b) What is the mode?
(c) Find the range.
(d) Compute the following:
(i) sample mean
(ii) sample median
(iii) sample variance
(iv) sample standard deviation
Find the z-scores of observations 2.05 and 3.95.
(f) Comment on the z-score values obtained in (e) above; specifically, where the two points are located relative to the sample mean.
(g) Is 3.95 an outlier? Is 2.05 an outlier? Explain.
(h) What is the shape of the distribution? Explain.
6. Consider the dataset below:
3, −5, 7, 4, 8, 2, 8, −3, −6
(a) What is the sample size?
(b) Calculate the sample mean.
(c) Find the sample median.
(d) What is the shape of the distribution? Explain.
(e) Find Q1 , Q2 , and Q3 .
(f) Calculate the inter-quartile range (IQR).
Calculate the fences.
(h) Does the fence test identify any outliers? Explain.
(i) Find the five-number summary. What is the five-number summary used for?
(j) Construct a boxplot and label it.
(k) Find P30 , P60 , and P90 .
(l) According to the empirical rule, what percentage of the observations in a data set that can be approximated by a normal curve lie within:
(i) one standard deviation of the mean?
(ii) two standard deviations of the mean?
(iii) three standard deviations of the mean?
2022-10-02