Exam 4: Numerical Descriptive Techniques

What statistics and graphs can you use to answer the following questions: Is the distribution unimodal,bimodal,or multimodal? If there is more than one mode,where are the peaks,and where are the valleys?

Pets Survey A sample of 36 families were asked how many pets they owned.Their responses are summarized in the following table. ​ ​ -{Pets Survey Narrative} Explain what the mean,median,and mode tell you about this particular data set.

How do the mean,median,and mode compare to each other when the distribution is: a.symmetric? b.negatively skewed? c.positively skewed?

Milk Demand ​ A supermarket has determined that daily demand for milk containers has an approximate bell shaped distribution,with a mean of 55 containers and a standard deviation of six containers. ​ ​ -{Milk Demand Narrative} If the supermarket begins each morning with a supply of 67 containers of milk,how often will demand exceed the supply? (Give a percentage.)

The ____________________ measures the margin of relative change in the dependent variable.

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 second quartile.

The smaller the spread of scores around 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} Describe the shape of the distribution of weights based on the quartiles' values.

In a negatively skewed distribution,the distance from the smallest observation to Q₁ exceeds the distance from Q₃ to the largest observation.

The ____________________ measures the spread between the middle 50% of the observations.

The ____________________ is the least desirable of all the measures of central location.

Test Scores ​ Suppose that an analysis of a set of test scores reveals that: Q₁ = 45,Q₂ = 85,Q₃ = 105. ​ ​ -{Test Scores Narrative} What can you say about the relative position of each of the observations 34,84,and 104,within this data set?

A basketball player has the following points for seven games: 20,25,32,18,19,22,and 30.Compute the following measures of variability. a.Standard deviation b.Coefficient of variation c.Compare the standard deviation and coefficient of variation and use them to discuss the variability in the data.

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} Determine the least squares line,and use it to estimate the value of y for x = 6.

Which of the following is a property of the slope,b₁?

If two data sets have the same standard deviation,they must have the same coefficient of variation.

Salaries of Employees ​ The following data represent the yearly 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,and 28.2. ​ ​ -{Salaries of Employees Narrative} Compute the mean salary.

The interquartile range is the difference between the:

If the observations are in the millions,a standard deviation of 10 would be considered small.If the observations are all less than 50,a standard deviation of 10 would be considered large.

Computers ​ The following data represent the number of computers owned by a sample of 10 families from Chicago: 4,2,1,1,5,3,0,1,0,and 2. ​ ​ -{Computers Narrative} Compute the median number of computers.