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PSU CHEM 003 - Chapters 2 and 3: Review Problem

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Chapters 2 and 3: Review Problems1. For each of the following measurements, identify whether the data are qualitative,discrete quantitative or continuous quantitative. Also, for each measurement, nameone statistic (e.g. average, percentage, median, range, etc.) that you might use tomake a summary statement about the measurement.(a) direction from class to your home (north, south, east, west, etc.)(b) number of words in a newspaper article(c) pulse rate (beats per minute)(d) birth order (first, second, third, etc.)(e) presence or absence of nausea(f) time it takes to shovel one’s driveway(g) number of siblings one has(h) body temperature (in degrees Fahrenheit)(i) color of a student’s backpack(j) degree of burn (first, second, third)2. Recorded here are the blood types of 40 persons who have volunteered to donateblood at a plasma center.O O A B A O A A A O B O B O OA O O A A A A AB A B A A O O AO O A A A O A O O AB(a) What is the type of the variable considered in this problem?(b) Summarize the data in a frequency table. Include calculations of the relativefrequencies.(c) Construct a Pareto Chart for the data set. (Pareto chart is bar chart withdecreasing height of the bars).3. The following are the numbers of passengers on the minibus tour of Hollywood.9 12 10 11 11 7 12 6 11 4 10 10 11 9 107 10 8 8 9 8 9 11 9 8 6 10 6 8 11(a) What is the type of the variable considered in this problem?(b) Display the data in a dotplot.(c) Comment on the shape of the distribution from the above dotplot.(d) Construct a frequency and relative frequency distributions.(e) Construct a histogram and comment on the shape of the distribution from thehistogram.4. A water-heater manufacturer guarantees the electric heating element for a period offive years. The lifetimes, in months, for a sample of 10 such elements are as follows.149.3 79.3 86.4 68.4 62.6 65.1 53.2 32.3 40.1 29.3(a) What is the type of the data?(b) Based on the above sample, make a statement about the corresponding “pop-ulation”. Also, write statements regarding the parameters µ and σ.(c) Display the data as a dotplot.(d) Draw Stem-and-Leaf Diagram for the data set.(e) Find Q1, M , Q3of the lifetimes. Interpret what each value means.(f) Construct a boxplot for the data set.(g) Is there any outlier? Change the maximum observation 86.4 to 126.4. Con-struct the boxplot again. Do you see any outlier now?(h) Using the positions of Q1, M, Q3in the boxplot, comment on the shape of thedistribution.(i) Find ¯x, s.(j) Write a statement using the computed value of ¯x. Does the computed value of¯x support the guarantee period?(k) What is the interpretation of the value of s.(l) Do you think the data follow an approximate bell-shaped, symmetric distribu-tion? Verify with empirical rule.(m) Construct a relative frequency distribution using 3 class intervals of equal widthstarting with the class interval “28 - under 48” – also written as [28, 48).(n) Plot the histogram using the relative frequency distribution obtained in the pre-vious part of this question. Locate ¯x, Q1, M , Q3on the histogram. Commenton the shape of the distribution based on the positions of ¯x and M.2Chapters 2 and 3: Solutions to Review Problems1. (a) Categorical (percentage)(b) Discrete Quantitative (average)(c) Continuous Quantitative (average), median range, standard deviation(d) Categorical (percentage)(e) Categorical (Percentage)(f) Continuous Quantitative (average, median, range, standard deviation)(g) Discrete Quantitative (average, mode)(h) Continuous Quantitative (average, median, range, standard deviation)(i) Categorical (percentage)(j) Categorical (percentage)2. Variable: Blood type(a) Categorical(b) The distribution table is given below.Blood type Frequency Relative FrequencyO 16 0.40A 18 0.45B 4 0.10AB 2 0.05Total 40 1.00(c) Pareto Chart for number of passengers is given below.A O B AB0.00.10.20.30.40.5Pareto Chart for Blood TypeBlood TypeRel. Frequency33. Variable: Number of passengers on the minibus tour of Hollywood(a) Discrete Quantitative(b) The dotplot for number of passengers is given below.4 6 8 10 12Dotplot of Number of Passengers(c) Shape of the distribution is skewed to the left.(d) n = 30, min = 4, max = 12Number of passengers Frequency Rel. Frequency4 1 0.0335 0 0.0006 3 0.1007 2 0.0678 5 0.1679 5 0.16710 6 0.20011 6 0.20012 2 0.067Total 30 1.001(e) The histogram for number of passengers is given below. Shape of the distribu-tion is skewed to the left.4 6 8 10 120.000.050.100.150.20Histogram for Number of PassengersNumber of PassengersRel. Frequency44. Variable: Lifetimes (in months) of the electric heating element(a) Continuous Quantitative.(b) Population: All electric heating elements ever produced by the water heatermanufacturer.µ: Actual (but unknown) mean (average) lifetime for all the electric heatingelements produced by the manufacturer.σ: Actual (but unknown) standard deviation of the lifetime for all the electricheating elements produced by the manufacturer.(c) Dotplot of the lifetime is given below.32 40 48 56 64 72 80Dotplot of Lifetimes(d) n = 10, min = 29.3, max = 86.4Stem Leaves Ordered Leaves2 9.3 9.33 2.3 2.34 9.3, 0.1 0.1, 9.35 3.2 3.26 8.4, 2.6, 5.1 2.6, 5.1, 8.47 9.3 9.38 6.4 6.4(e) n = 10, Location for the median =n+12= 5.5So, M = Average of 5th and 6th ordered observations =53.2+62.62= 57.9Q1= Median of the lower half of the observations.There are 5 observations in the lower half.So, location for the Q1=n+12= 3 andQ1= 3rd observation in the arranged data (counting forward) = 40.1.Then, Q3= 3rd observation in the arranged data (counting backward) = 68.4.So, Q1= 40.1, M = 57.9, Q3= 68.4.Interpretation: 25% of the electric heating elements lasted less than 40.1months, 50% of the electric heating elements lasted less than 57.9 months and75% of the electric heating elements lasted less than 68.4 months.5(f) IQR = Q3− Q1= 68.4 − 40.1 = 28.3Lower limit = Q1− (1.5)(IQR) = 40.1 − 1.5(28.3) = −2.35Upper limit = Q3 + (1.5)(IQR) = 68.4 + 1.5(28.3) = 110.85.Potential outlier: NoneAdjacent values: 29.3, 86.4.The boxplot is given below.Boxplot for Lifetimes30 40 50 60 70 80 90(g) There is no outlier. When 86.4 is changed to 126.4, 126.4 becomes an outlier(since it exceeds the upper side provision of 110.85). Then, boxplot would beas follows.*Boxplot for Lifetimes30 40 50 60 70 80 90 100 110 120 130(h) Since M is (little) closer to Q3, than Q1, the distribution is (a little) skewed tothe left.(i) n = 10,Px = 566,Px2=


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