Exam 4: Numerical Descriptive Techniques

Which of the following statements is true?

The precision provided by the numerical techniques (mean,median,and standard deviation)provides more useful information than graphical techniques (histograms and box plots)alone.

The line drawn within the box of a box plot always represents the median.

Given the following sample data: ​ 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.

In a histogram,the proportion of the total area which must be to the left of the median is more than 0.50 if the distribution is positively skewed.

Which of the following characteristics does a histogram help you identify?

In a positively skewed distribution,the percentage of data between the smallest observation and Q₁ is less than the percentage of data between Q₃ and the largest observation.

Chebysheff's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is at least 96%.

Which of the following statistics is a measure of central location?

Which of the following summary measures is sensitive to extreme values?

Which of the following statements is true regarding the data set 8,8,8,8,and 8?

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

Weights of Teachers ​ The following data represent the weights in pounds of a sample of 25 teachers: 164,148,137,157, 173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140, and 171. ​ ​ -{Weights of Teachers Narrative} Which is a better measure of variability in the weights of the teachers,the standard deviation or the coefficient of variation?

Yearly Donations ​ The following data represent the yearly donations (in thousands of dollars)of a sample of 13 benefactors: 26.5,23.5,29.7,24.8,21.1,24.3,20.4,22.7,27.2,23.7,24.1,24.8,and 28.2. ​ ​ -{Yearly Donations Narrative} Compute and interpret the 90th percentile.

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​ -{2-Year Investment Narrative} Compare the values of the arithmetic and geometric means.

Which of the following statements about the median is not true?

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​ -{2-Year Investment Narrative} Calculate the geometric mean.

Ages of Volunteers ​ The following data represent the ages in years of a sample of 25 volunteers from a charitable organization: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35, and 20. ​ ​ -{Ages of Volunteers Narrative} Compute the range of the data and express the number in the appropriate unit.

The mean is affected by extreme values but the median is not.