Exam 4: Numerical Descriptive Techniques

The coefficient of variation allows us to compare two sets of data based on different measurement units.

Weights of Police Officers ​ The following data represent the weights in pounds of a sample of 25 police officers: 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 Police Officers Narrative} Construct a frequency distribution for the data,using five class intervals,and the value 130 as the lower limit of the first class.

The variance is a measure of the linear relationship between two variables.

Scatter diagrams,covariance,and the coefficient of correlation are useful techniques for detecting relationships between two ____________________ variables.

The magnitude of the correlation measures the ____________________ of a linear relationship.

The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2.

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 median.

If the correlation coefficient r = 1.00,then all the observations must fall exactly on:

According to the Empirical Rule,if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 1 standard deviation around the mean.

We can frequently make several inferences about the nature of the data from the ____________________ of its histogram.

Is it possible for the standard deviation of a data set to be larger than its variance? Explain.

Longevity and Salary A sample of eight observations of variables x (years of experience)and y (salary in $1,000s)is shown below: ​ ​ -{Longevity and Salary Narrative} Draw the scatter diagram and plot the least squares line.

The variance is more meaningful and easier to interpret compared to the standard deviation.

Three measures of the linear relationship between x and y are the coefficient of correlation,the coefficient of determination,and the coefficient of variation.

____________________ are extremely large or extremely small observations.

Hours of Playing Video Games ​ Suppose that the following data provide the hours of playing video games per week for a sample of 15 high school students in Roanoke,Virginia: 5,11,25,19,18,20,27,13,8,10,15,19,18,9,and 12. ​ ​ -{Hours of Playing Video Games Narrative} Determine the location and value of the first quartile.

If cov(x,y)= 20, then the sample coefficient of correlation r is:

According to Chebysheff's Theorem,at least 93.75% of observations should fall within 4 standard deviations of the mean.

Weights of Police Officers ​ The following data represent the weights in pounds of a sample of 25 police officers: 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 Police Officers Narrative} Determine the location and value of the 60th percentile of the weights.

Strip Mall Rent ​ Monthly rent data in dollars for a sample of 10 stores in a small town in South Dakota are as follows: 220,216,220,205,210,240,195,235,204,and 250. ​ ​ -{Strip Mall Rent Narrative} Compute the sample monthly average rent.