Exam 5: Numerical Descriptive Measures

When approximating descriptive measures for grouped data, the sample mean can be obtained by making the assumption that the midpoint of each class closely approximates the mean of each class.

Chebyshev's theorem relates to only to symmetric histograms.

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

Which of the following statements best describes the mean of a data set?

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Melbourne: 3 3 2 2 4 5 2 5 4 2 Use these data to answer the following question/s. -a. Compute the range. b. Compute the variance. c. Compute the standard deviation.

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55. Using Chebyshev's theorem, at least 75% of the sales receipts were between $44.65 and $86.85.

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.

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 variance and standard deviation of the salaries.

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 sample variance and sample standard deviation.

When approximating descriptive measures for grouped data, the shape of the distribution within each class is ignored.

Data from three samples are shown below: Sample A: 17 22 20 18 23 Sample B: 30 28 35 40 25 Sample C: 44 39 54 21 52 Examine the three samples. Without performing any calculations, indicate which sample has the greatest amount of variability and which sample has the least amount of variability.

Which of the following summary measures is affected by extreme values?

Compute the coefficient of variation.

The coefficient of correlation indicates the direction and the strength of the linear relationship between two 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 Calculate the 4th decile of the data.

A sample of 12 measurements has a mean of 25 and a standard deviation of 4. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 25. a. Find the mean of the sample of 14 measurements. b. Find the standard deviation of the sample of 14 measurements.

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?

Which measure of variability is appropriate when a sample is likely to contain one or several extreme values?

Monthly rent data in dollars for a sample of 10 one-bedroom apartments in Perth are given below: 220 200 230 215 235 250 260 210 265 250 a. Compute the sample monthly average rent. b. Compute the sample median. c. What is the mode?

The relative frequency histogram for the age (in years) of a sample of 25 employees from a government department, is given below. Explain what the best measure of central location is.