Exam 4: Numerical Descriptive Techniques

In a histogram, the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.

If a data set contains an even number of observations, the median is found by taking the ____________________ of these two numbers.

NARRBEGIN: Ages of Senior Citizens 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.NARREND -{Ages of Senior Citizens Narrative} Calculate the median age of the uninsured senior citizens.

Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?

NARRBEGIN: Ages of Retirees Ages of Retirees A sociologist recently conducted a survey of retirees 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 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.NARREND -{Ages of Retirees Narrative} Calculate the first quartile of the ages of the uninsured retirees.

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%.

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.

Statisticians typically apply graphical techniques as a first step in a data analysis because we first need to know the shape of the distribution.

NARRBEGIN: Experience and Salary Longevity and Salary A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below: 5 3 7 9 2 4 6 y 20 23 15 11 27 21 17 14 NARREND -How is the value of the correlation coefficient r affected in each of the following cases? a.Each x value and y is multiplied by 4. b.Each x value is switched with the corresponding y value. c.Each x value is increased by 2.

NARRBEGIN: Children 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.NARREND -{Computers Narrative} Is the distribution of the number of computers symmetric or skewed? Why?

The techniques of shrinking the horizontal axis or stretching the vertical axis have the effect of making the slope of the graph visually (but not numerically) steeper.

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

A scatter diagram reveals a strong positive linear relationship between oil and gasoline prices. Which of the following numerical techniques will not give us more detailed information about this relationship?

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

NARRBEGIN: Experience and Salary Longevity and Salary A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below: 5 3 7 9 2 4 6 y 20 23 15 11 27 21 17 14 NARREND -Consider the following data: 9 6 7 5 8 y 19 14 16 12 15 a.Calculate the covariance and the coefficient of correlation for the sample. b.What do these statistics tell you about the relationship between x and y?

NARRBEGIN: Ages of Workers Ages of Workers The ages (in years) of three groups of workers are shown below: GROUP A: 17 22 20 18 23 GROUP B: 30 28 35 40 25 GROUP C: 44 39 54 21 52 NARREND -The number of hours a college student spent studying during the final exam week was recorded as follows: 7, 6, 4, 9, 8, 5, and 10. Compute s² and s for the data and express the numbers in the appropriate unit.

NARRBEGIN: Weights of Workers 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.NARREND -The number of hours a college student spent studying during the final exam week was recorded as follows: 7,6, 4, 9, 8, 5, and 10. Compute $\bar { x }$ for the data and the value in an appropriate unit.

In a perfectly symmetric distribution, which of the following statements is false?

The smaller the spread of scores around the mean:

The coefficient of correlation and the least squares line both describe the relationship between two interval variables.