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 sample mean weight.

Which of the following are measures of the linear relationship between two variables? A The covariance. B The coefficient of correlation. C The coefficient of determination. D All of these choices are correct.

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 Calculate the 3rd and 8th deciles of the data.

In a negatively skewed distribution, the mean is smaller than the median and the median is smaller than the mode.

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

Using percentiles, the difference between which of the following is the interquartile range? A 10 \% and 90\% values. B 25\% and 75\% values. C 15\% and 85\% values. D 30\% and 70\% values.

Quartiles divide the values in a data set into four parts of equal size.

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 coefficient of determination may range in values between negative one and positive one.

When a distribution is symmetric, the mean, median and the mode are all equal.

The least squares method is the method of deriving a linear equation between two numerical variables.

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 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 Draw the scatter diagram and plot the least-squares line.

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 The frequency distribution for the data, using five class intervals and the value 20 as the lower limit of the first class is given below. Class Limits Frequency 20 up to 30 4 30 up to 40 7 40 up to 50 9 50 up to 60 3 60 up to 70 2 Total 25 Find the mean of the grouped data.

When the distribution is skewed, the interquartile range is a better measure of variability than the standard deviation.

Which measure of variability is appropriate when a sample is likely to contain one or several extreme values? A The variance. B The standard deviation. C The interquartile range. D The range.

Given the following sample data: x 420 610 625 500 400 450 550 650 480 565 y 2.80 3.60 3.75 3.00 2.50 2.70 3.50 3.90 2.95 3.30 a. calculate the covariance and the correlation coefficient. b. comment on the relationship between X and Y. c. determine the least-squares line. d. draw the scatter diagram and plot the least-squares line.

The coefficient of determination measures the percentage of variation in the independent variable explained by the dependent variable.

If the coefficient of correlation r = 0, then there is no linear relationship between the dependent variable y and the independent variable x.

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 upper quartile of the ages.