Ans - 1 Wk - Examining Distributions - 2

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Statistics

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Jan 9, 2024

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Name: ________________________________ Statistics | Rutgers-Newark | Saleh 1 – Examining Distributions Each of the following two histograms represents the distribution of acceptance rates among 25 business schools in 2015. The histograms use different class intervals, but are based on the same data. In each class interval, the left endpoint is included but not the right. 1. Which interval contains more than half of all the observations? A) 20%  acceptance rate < 35% C) 35%  acceptance rate < 50% B) 7.5%  acceptance rate < 30% D) 30%  acceptance rate < 45% The following are the salaries (in thousands of dollars) of 20 employees for this year. Data are ordered for convenience. 28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77 2. The five-number summary is: Min = 28 Q1 = (37+41)/2 = 39 M = (47+49)/2 = 48 Q3 = (60+61)/2 = 60.5 Max =77 3. The IQR of the 20 salaries = Q3 – Q1 = 60.5 – 39 = 21.5 4. Sketch or use Excel to construct a boxplot of the data above:

5. The standard deviation of 16 measurements of people's weights (in pounds) is computed to be 5.4. The variance of these measurements = (standard deviation) 2 = 5.4 2 = 29.16 6. A sample of 12 measurements has a mean of 38 and a standard deviation of 4.25. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 38 each. A. Would the mean change? No . → → B. The standard deviation of the 14 measurements = 2 1 ) ( 1 1 x x n s n i − − =  Plug in given values → Solve for the sum of the squares → Then add in (sum) the square of the deviation from the mean - 38) 2 of the two additional values (38 & 38) Sum of the squares (now) = 198.687 + (38-38) 2 + (38-38) 2 = 198.687 7. For the density curve above, what percent of the observations lie above 1.8? 2.0-1.8 = 0.2 → (0.2 / 2.0) * 100 = 10% 8. For the density curve above, what percent of the observations lie between 0.4 and 1.1? [(1.1-0.4) / 2.0] * 100 = 35%

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