1. A survey of students resulted in the data summarized in the frequency distribution shown inTable 1. Use this information to answer the following. Table 1: Hours Students Watch TV in a Week Class Frequency 1214 20 2110 29 3011 38 394 47 484 56 (a) What is the class width (support answer with a calculation)? (b) Add to the original table by completing the blank cells as indicated. Table 2: Hours Students Watch TV in a Week LCB UCB Midpoint Freq Relative Frequency Cumulative Frequency 14 10 11 4 4 (c) Find the mean, variance, and standard deviation for this grouped data. You must show all work including symbols, formulas and calcuations. You may find the table below useful to organize your calculation. Table 3: Hours Students Watch TV in a Week Class Frequency X f f X X Midp m 2 m m oint 2 (m) Totals() Mean: Variance: Standard deviation: Table 4: Sampled Weights Ste Leaf m 9 8 10 1 3 7 11 4 4 5 6 9 12 1 2 7 13 1 6 2. The following Stem and Leaf Plot represents the distribution of weights for a group of women. (a) Describe the shape of the distribution in terms of symmetry, skew (if any), and numberof modal classes (not by specific value). (b) Mode(s), and Modal class, if any. (c) Median(s), if any. (d) What conditions should be met for range rule of thumb to be a reasonable estimate of standard deviation? Are the conditions met? (e) What is the range for the data? (f) What estimate does range rule of thumb provide for standard deviation? (g) Don't calculate mean or standard deviation, but use mean as 115 pounds and standard deviation 10 pounds. According to Chebyshev's Rule, what can be said about the the fraction or percentage of data that lies between 100 pounds and 130 pounds? (Hint: You will need to find the value of \"k\" that accounts for this range. It is NOT 2 or 3). What is the actual fraction or percentage of the data in this range? (Just count then divide by total number in sample). Is Chebyshev's Rule satisfied Yes or No? (h) State the requirement(s) needed for Empirical rule to apply. Are these conditions met? Yes or No. Estimate the percentage of data between 105 pounds and 125 pounds? What is the actual percentage of data in the range? (Don't be alarmed if the prediction is off by around 10%). 3. The data below represents measurements of length in inches of 12 caterpillars: 5,3,5,8,7,2,9,5,4,6,5,6. (a) Find the 5 number summary for the data. (b) Determine the interquartile range, IQR. (c) Which points (if any) should be considered outliers? (Hint: use IQR to calcuate lowerand upper fences). 4. Tom is 72 inches tall and Jane is 67 inches tall. Both are above average in height. (a) Calculate Z-score for each based on the data below. Then determine who is taller withrespect gender? Assume the mean height for men is 70 inches with standard deviation of 5 inches; mean height for women is 64 inches with standard deviation of 4. (b) Based on the parameters listed in part a above, calculate coefficient of variation (CV). Based on CV which gender has more variation? 5. Possible answers are listed below: (a) This branch of statistics is mostly concerned with characterizing data. (b) Branch of statistics which includes hypothesis testing: (c) Arguably the best measure of center, but can be influenced by extreme values: (d) A measure of center which tends to be stable in presence of extreme values: (e) This measure of variability has same units as original data and is based on averge squareddistance from mean. (f) A value characterizing a population. (g) A value characterizing a sample. Possible answers: statistic, mutually exclusive, independent, mean, median, midrange, standard deviation, variation, classical probability, empirical probability, inferential statistics, descriptive statistics, parameter, range