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Math
Statistics
CH 3-4 HW Questions Review
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When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will __________________. (3.1)
Increase
The U.S. Department of Housing and Urban Development (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the median? (3.1)
HUD uses the median because the data are skewed right.
A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why? (3.1)
The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.
True or False: A data set will always have exactly one mode. (3.1)
FALSE
Determine if the statement is true or false. When an observation that is much larger than the rest of the data is added to a data set, the value of the median will increase substantially. (3.1)
FALSE
For a distribution that is skewed left, which of the following is true? (3.1)
Mean < Median
The standard deviation is used in conjunction with the ______ to numerically describe distributions that are bell shaped. The ______ measures the center of the distribution, while the standard deviation measures the ______ of the distribution. (3.2)
Mean-Mean-Spread
True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. (3.2)
True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
What makes the range less desirable than the standard deviation as a measure of dispersion? (3.2)
The range does not use all the observations.
In a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.5 inches and the standard deviation of females was 3.2 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately? (3.2)
The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion.
What can be said about a set of data with a standard deviation of 0? (3.2)
All the observations are the same value.
The standard deviation can be negative. (3.2)
FALSE
If the variance of a variable is 9, what is the standard deviation? (3.2)
3
If the standard deviation of a variable is 12, what is the variance? (3.2)
144
Suppose the first class in a frequency table of quantitative data is 0-4 and the second class is 5-9. What is the class midpoint of the first class? (3.3)
2.5
The _______ represents the number of standard deviations an observation is from the mean. (3.4)
Z-Score
_______ divide data sets in fourths. (3.4)
Quartiles
What does it mean to say that two variables are positively associated? Negatively associated? (4.1)
---There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases.
---There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases
What does it mean to say that the linear correlation coefficient between two variables equals 1? What would the scatter diagram look like? (4.1)
---When the linear correlation coefficient is 1, there is a perfect positive linear relation between the two variables.
---The scatter diagram would contain points that all lie on a line with a positive slope.
What does it mean if r = 0? (4.1)
No linear relationship exists between the variables.
If the linear correlation between two variables is negative, what can be said about the slope of the regression line? (4.2)
Negative
What is a residual? What does it mean when a residual is positive?
---A residual is the difference between an observed value of the response variable y and the predicted value of y.
---If it is positive, then the observed value is greater than the predicted value.
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