Consider the following sample of numbers: 16,5,12,15,9,19 Using the above sample, answer the following questions. Where relevant. round your answer to three decimal places. a. What is the mean? b. What is the median\"? Suppose a sample of n = 77 observations was taken and the sample variance was calculated to be 1190.25. What is the sample standard deviation? Where relevant, round your answer to three decimal places. Answer: Suppose a sample of n = 77 students were asked their height in cm. Some summary statistics are provided below. You will need one or more of these to answer the question that follows. - lvlean = 170.4 - Standard deviation = 9.268 - Variance = 85.894 o Q1 =164.274 02 = 170.481 o QB =177.052 What is the IQR'? Where relevant. round your answer to three decimal places. Answer: Consider the distribution of the data represented in the above histogram. Based on the histogram, which of the below statements isfare true? Select one or more: :I a. The distribution is positively skewed '_] b. The distribution is skewed to the right :1 c. The distribution is roughly symmetric :l d. The distribution is skewed to the left :I e. The distribution is negatively skewed Below are six different scatterplots. These scatterplots are labelled 'Scatterplot A', 'Scatterplot B', 'Scatterplot C', 'Scatterplot D', 'Scatterplot E' and 'Scatterplot F', respectively. Note that in the answers below, they are referred to in abbreviated fashion, i.e. 'A', 'B', 'C', 'D', E', and 'F' respectively. Scatterplot A Scatterplot B Scatterplot C Scatterplot D Scatterplot E Scatterplot F In a random order, the correlations (r) associated with these scatterplots are 0.29, -0.64, 0.65, -0.85, 0.84, and -0.28. Your task is to study the scatterplots and then to match each scatterplot with its correct correlation. Each correlation belongs to just one scatterplot. When you are confident with your answers then choose the correct choice below. Select one: O a. A:r = -0.28; B: r = 0.65; C:r = 0.84; D: r = -0.64; E: r = -0.85; F:r = 0.29 O b. A: r = 0.65; B: r = -0.28; C: r = 0.84; D: r = -0.64; E: r = -0.85; F: r = 0.29 O c. A: r = -0.28; B: r = 0.65; C: r = 0.84; D: r = -0.85; E: r = -0.64; F: r =0.29 O d. A: r = -0.28; B: r = 0.84; C:r = 0.65; D: r = -0.64; E: r = -0.85; F: r = 0.29 O e. A: r = -0.28; B: r = 0.29; C: r = 0.84; D: r = -0.64; E: r = -0.85; F: r = 0.65Suppose you wish to describe the data represented in the above histogram using a measure of location. Which measure is preferable? Select one: Q a. Mean 0 b. Median O 0. [OR '3 d. Standard deviation e. Skevvness l... Suppose you wish to describe the data represented in the above histogram using a measure of spread. Which measure is preferable? Select one: C) a. Standard deviation 0 b. lQR O 0. Mean 0 d. Median C) e. Skevvness Four plots are displayed below. Each plot displays a normal probability density function with a different value of ,u for each. These plots are labelled 'Plot t\". \"Plot 8', 'Plot (3' and \"Plot 0', respectively. Plot A Plot B Densy 002 004 Densy 002 004 000 000 20 30 40 50 60 TD 80 90 80 ?U 50 5D 40 30 X X Plot C Plot 0 004 004 Densy 002 Dansy 002 000 000 -20 -1D 0 10 20 30 40 10 20 30 40 50 EU ?0 X X In random order. the values of pt in each of the plots above are 50. 40. 60 and 10 respectively. Your task is to study the plots and then to match each plot with its correct mean (pa). Each mean belongs tojust one plot. When you are confident with your answers then choose the correct choice below. Select one: Q 3. Plot A: p, = 50;;Plot 13: pi = 60;;Plot C: pi = 10; ;Plot D: ,u, = 40 C) b. Plot A: p = 50; ; Plot 13: p = 40; ; Plot C: ,u = 10; ;Plot D: p = 60 C c. Plot A: p, = 50; ; Plot B: pi = 10; ; Plot C: ,u. = 60; ;Plot D: ,u, = 40 {j d. Plot A: p = 50; ; Plot 13: p = 60;;P1o1: C: ,u. = 40; :Plot D: p, = 10 C e. Plot A: p, = 60;;Plot B: pi, = 50;;P1ot C: ,u. = 10; ;Plot D: ,u, = 40 Four plots are displayed below. Each plot displays a normal probability density function with a different value of o- for each. These plots are labelled 'Plot A', \"Plot B'. 'Plot {3' and \"Plot D', respectively. PlotA PlotB 'u' 8. 3: D 3: E E N E C 3 8. 8 D 8 S C? D. D D -300 -200 400 0 100 200 300 -50 U 50 x x PIOtC PlotD .. '2' :h-i. 3:. D 7:2 g a N 3 :5 do 3 D D C 8. 3. D D 200 400 U 100 200 QUE) -1UU U 100 200 X X In random order. the values of 0 in each of the plots above are 80, 75, 25 and 60 respectively. Your task is to study the plots and then to match each plot with its correct standard deviation (0). Each standard deviation belongs to just one plot. When you are confident with your answers then choose the correct choice below. Select one: C: a. Plot A: 0' = 80; ; P101: B: 0' = 25;;P10t C: 0 = 60; :Plot D: 0' = 75 O b. Plot A: 0' = 80; ; P101: B: 0' = 60;;P10t C: 0 = 25; :Plot D: 0' = 75 O C. Plot A: 0' = 80; ; P101: B: 0' = 25;;Plot C: 0 = 75; ;Plot D: 0' = 60 Q d. Plot A: 0' = 25; ; P101: B: 0' = 80;;Plot C: 0 = 60; ;Plot D: 0' = 75 C) e. Plot A: 0' = 80; ; P101: B: 0' = 75;;P10t C: 0 = 60; :Plot D: 0' = 25 Suppose X w N(12.83, 4.12). For a value of a: = 28, what is the corresponding zscore? Where relevant, round your answer to three decimal places. Answer: Density 0.000 0.002 0.004 0.008 0.008 0.010 0 50 100 1 50 200 250 300 The above plot displays the normal probability density function for a random variable X m N(150,40). The shaded area represents P(X S 178) : 0.758. What must P(X 2 178) be equal to? Where relevant, round your answer to three decimal places. Answer: Density 0.000 0.002 0.004 0.008 0.005 0.010 0 50 100 1 50 200 250 300 The above plot displays the normal probability density function for a random variable X ~ N(150, 402). The blue shaded area represents P(150 1.283 X 40 g X g 150 + 1.283 x 40) : P(98.68 g X s 201.32) : 0.801 . In other words, the blue shaded area represents the probability that X is within1.283 standard deviations of the mean. What must be the combined value of both areas shaded in red? Where relevant, round your answer to three decimal places