b s can never be zero c s is a good measure of spread in the presence of

B s can never be zero c s is a good measure of spread

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b) s can never be zero. c) s is a good measure of spread in the presence of outliers Problem 10: Consider 10 sample points x 1 , x 2 , …, x 10 , with 𝑥 𝑖 = 100 10 𝑖=1 and 𝑥 𝑖 2 = 1294 10 𝑖=1 (a) Compute the sample mean and the sample standard deviation of the data? (b) If a new data point x 11 =10 is added to the sample. What are the new sample mean and sample standard deviation of the 11 data points? Problem 11: A company wants to investigate the amount of sick leave taken by its employees. A sample of 8 employees yields the following numbers of sick leave (in days) taken over the past year: 0 0 4 0 0 0 6 0 a) What is the range of the data? b) Compute the sample standard deviation of the data. c) It turns out that the data value 6 was recorded incorrectly, with the correct value given by 60. Redo part a) and b) based on the correct data, and describe the effect of the outlier. Problem 12: Consider a sample of 10 data points x 1 , x 2 , …, x 10 , with sample mean, mode, sample standard deviation and range given by 10, 12, 4 and 13 respectively. If we transform the data through the formula y i = 10 x i +2. What are the sample mean, mode, sample standard deviation and range of y 1 , y 2 , …, y 10 ? Problem 13: Compute the sample variance of the 10 data points: -20, 20, -30, 10, -20, -10, 20, 10, 20, 10 Problem 14 : It’s known that the sample variance and range of x 1 , x 2 , …, x 100 are 21 and 10 respectively. If we transform the data through y i = -2 x i +5, what are the sample variance and the range of y 1 , y 2 , …, y 100 ?
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