A time series graph plots data values in the order they were recorded over time.
Correct Answer
True
True. A time series graph places time on the horizontal axis and the measured values on the vertical axis, which shows trends over time.
Category: Graphing Data
Question 2
The median of a data set is its 50th percentile.
Correct Answer
True
True. Half of the ordered data fall at or below the median, so it is the 50th percentile and also the second quartile.
Category: Measures of Location
Question 3
About 25% of the values in a data set lie between the first quartile and the median.
Correct Answer
True
True. The first quartile cuts off the lowest 25% of the data and the median cuts off the lowest 50%, so about 25% of the values lie between them.
Category: Measures of Location
Question 4
The standard deviation is expressed in the same units as the original data.
Correct Answer
True
True. Taking the square root of the variance returns the spread to the original units, so the standard deviation of heights in inches is also in inches.
Category: Measures of Spread
Question 5
In a symmetric distribution, the mean and the median are approximately equal.
Correct Answer
True
True. With no long tail on either side, nothing pulls the mean away from the middle, so the mean and the median are about the same.
Category: Skewness
Question 6
To find a sample variance, the sum of the squared deviations is divided by n - 1.
Correct Answer
True
True. The sample variance divides by n - 1, one less than the sample size. The population variance divides by N, the size of the population.
Category: Measures of Spread
Question 7
A single outlier can greatly increase the standard deviation of a data set.
Correct Answer
True
True. The standard deviation uses every deviation from the mean, and squaring a very large deviation makes it count heavily, so one extreme value can inflate it.
Category: Measures of Spread
Question 8
A frequency polygon plots the frequency of each interval above the interval's midpoint and joins the points with line segments.
Correct Answer
True
True. A frequency polygon shows the same information as a histogram by connecting points placed at the midpoints of the intervals.
Category: Graphing Data
Question 9
The variance of a data set is measured in the square of the data's units.
Correct Answer
True
True. The variance averages squared deviations, so data in centimeters have a variance in square centimeters.
Category: Measures of Spread
Question 10
A z-score of 0 means the data value is equal to the mean.
Correct Answer
True
True. A z-score counts how many standard deviations a value is from the mean, so a value with no distance from the mean has a z-score of 0.
Category: Z-Scores and Empirical Rule
Question 11
In a right-skewed distribution, the mean is usually less than the median.
Correct Answer
False
False. In a right-skewed distribution, the long tail of high values pulls the mean upward, so the mean is usually greater than the median.
Category: Skewness
Question 12
The range is resistant to outliers because it depends only on the middle of the data.
Correct Answer
False
False. The range is the maximum minus the minimum, so it depends entirely on the two most extreme values and is strongly affected by outliers.
Category: Measures of Spread
Question 13
The standard deviation can be negative when most data values are below the mean.
Correct Answer
False
False. The standard deviation is the square root of an average of squared deviations, so it is always positive or zero.
Category: Measures of Spread
Question 14
A data set can have only one mode.
Correct Answer
False
False. A data set can have more than one mode. When two values tie for the highest frequency, the data set is bimodal.
Category: Measures of Center
Question 15
In a data set of 9 values, raising the largest value from 50 to 500 changes the median.
Correct Answer
False
False. The median of 9 ordered values is the 5th value, which stays the same when only the largest value changes. The mean, by contrast, would increase.
Category: Measures of Center
Question 16
A potential outlier should be removed from a data set without further investigation.
Correct Answer
False
False. A potential outlier should be investigated first. It may be a recording error, but it may also be a real and important value.
Category: Measures of Location
Question 17
A test score with a z-score of -2 is 2 points below the class mean.
Correct Answer
False
False. A z-score of -2 means the score is 2 standard deviations below the mean, not 2 points. If the standard deviation were 5 points, the score would be 10 points below the mean.
Category: Z-Scores and Empirical Rule
Question 18
The empirical rule applies to every data set, whatever the shape of its distribution.
Correct Answer
False
False. The empirical rule applies only to bell-shaped, symmetric distributions. Chebyshev's rule is the one that holds for any shape.
Category: Z-Scores and Empirical Rule
Question 19
A data set with a larger standard deviation has values clustered more tightly around the mean.
Correct Answer
False
False. A larger standard deviation means the values are more spread out from the mean. Values clustered tightly around the mean give a small standard deviation.
Category: Measures of Spread
Question 20
The mean of the values 2, 4 and 9 is 4.
Correct Answer
False
False. The mean is (2 + 4 + 9) / 3 = 15 / 3 = 5. The value 4 is the median, the middle value of the ordered data.
Category: Measures of Center