Exam 4: Numerical Descriptive Techniques

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} Calculate the 3rd and 7th deciles of the data.

Ages of Senior Citizens ​ A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92, 94,and 97. ​ ​ -{Ages of Senior Citizens Narrative} Calculate the median age of the uninsured senior citizens.

The 10th ____________________ is the value for which 10% of the observations are less than that value.

A sample of 13 college professors has a mean age of 30 years and a standard deviation of 5 years.Suppose that the sample is enlarged to 15 college professors,by including two additional professors that are each 30 years old.Will the standard deviation increase,decrease,or stay the same,and why?

Weights of Workers ​ The following data represent the number of employees of a sample of 25 companies: 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 Workers Narrative} Find the median number of workers.

Which measures of central location and variability are considered to be resistant to extreme values?

When extreme values are present in a set of data,which of the following descriptive summary measures are most appropriate?

Chebysheff's Theorem applies only to data sets that have a bell shaped distribution.

The length of the box in the box plot portrays the:

Which measure(s)of central location is/are meaningful when the data are ordinal?

The interquartile range is a measure of variability in a set of data.

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} a.Describe the shape of distribution of donations based on the values of the quartiles. b.Give a possible reason for the shape of this data set,in terms of donations.

The distance between the 25th percentile and the median is always the same as the distance between the median and the 75th percentile.

The interquartile range will always exceed that of the range.

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} What does the histogram tell you about the distribution of the weights of workers?

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 second quartile of the weights.

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} Calculate and interpret the interquartile range.

Ages of Jockeys ​ The following data represent the ages in years of a sample of 25 jockeys from a local race track: 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 Jockeys Narrative} a.Construct a box plot for the ages and identify any extreme values. b.What does the box plot tell you about the distribution of the data?

A population with 200 elements has a variance of 20.From this information,it can be shown that the population standard deviation is 10.

The value of the standard deviation may be either positive or negative,while the value of the variance will always be positive.