Exam 5: Numerical Descriptive Measures

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight 165 175 150 155 173 149 145 153 153 153 152 145 164 143 170 175 148 174 171 156 166 168 152 150 173 168 146 155 172 159 Compute the range and interquartile range of the data.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Find the range of ages.

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 50% of deliveries take more than 5 hours?

A sample of eight observations of variables x and y is shown below: x 5 3 7 9 2 4 6 8 y 20 23 15 11 27 21 17 14 Calculate the covariance and the coefficient of correlation, and comment on the relationship between X and Y.

The range is considered the weakest measure of variability.

A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of 6 cartons. a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61? b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean? c. If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand?

How is the value of the correlation coefficient r affected in each of the following cases? a. Each x value is multiplied by 4. b. Each x value is switched with the corresponding y value. c. Each x value is increased by 2.

When is the standard deviation of a data set smaller than its variance? Explain.

The empirical rule states that the percentage of observations in a data set (provided that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is approximately 75%.

Suppose that an analysis of a set of data reveals that $Q _ { 1 } = 45,$ $Q _ { 2 } = 85$ and $Q _ { 3 } = 105$ a. What do these statistics tell you about the shape of the distribution? b. What can you say about the relative position of each of the observations 34, 84 and 104? c. Calculate the interquartile range. d. What does the interquartile range tell you about the data?

Chebyshev's theorem states that the percentage of observations in a data set that should fall within 3 standard deviations of their mean is at least 88.9%.

The coefficient of variation gives an indication of the magnitude of the standard deviation relative to the mean.

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Compute the 8th decile of the data.

Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one.

The shape of the distribution helps to determine the best measure of central location and variability in a data set.

A linear regression model estimating the relationship between Expenditure on imports ($) and Annual household income ($) is as follows: Estimated Expenditure on Imports = 1.35 + 0.11Annual household income. Interpret the slope.

A linear regression model estimating the relationship between Expenditure on Imports and Annual household income has an R2 value of 0.81. Interpret R2.

In a symmetric distribution, the mean is the most used measure of central location for quantitative data.

A data sample has a mean of 107, a median of 122 and a mode of 134. The distribution of the data is positively skewed.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: 26.5 23.5 29.7 24.8 21.1 24.3 20.4 22.7 27.2 23.7 24.1 24.8 28.2 Compute the coefficient of variation.