Describing the Distribution of Quantitative Variables - AP Statistics
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What graphical display is best for showing data distribution?
What graphical display is best for showing data distribution?
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Histogram. Shows frequency distribution using bars for different value ranges.
Histogram. Shows frequency distribution using bars for different value ranges.
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Identify the term for data represented by a single peak.
Identify the term for data represented by a single peak.
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Unimodal. Distribution has exactly one peak or mode.
Unimodal. Distribution has exactly one peak or mode.
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What is the term for the average of the squared deviations?
What is the term for the average of the squared deviations?
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Variance. Standard deviation squared, measuring spread around the mean.
Variance. Standard deviation squared, measuring spread around the mean.
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What is the five-number summary of a data set?
What is the five-number summary of a data set?
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Minimum, Q1, Median, Q3, Maximum. These five values completely describe the data's position and spread.
Minimum, Q1, Median, Q3, Maximum. These five values completely describe the data's position and spread.
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State the formula for calculating the variance of a data set.
State the formula for calculating the variance of a data set.
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$\frac{\sum (x_i - \bar{x})^2}{n-1}$. Average of squared deviations from the mean, using n-1 denominator.
$\frac{\sum (x_i - \bar{x})^2}{n-1}$. Average of squared deviations from the mean, using n-1 denominator.
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Identify the term for the spread of the entire data set.
Identify the term for the spread of the entire data set.
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Range. Measures the distance between maximum and minimum data values.
Range. Measures the distance between maximum and minimum data values.
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What is a characteristic of a uniform distribution?
What is a characteristic of a uniform distribution?
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All values have approximately the same frequency. Each outcome occurs with roughly equal probability or frequency.
All values have approximately the same frequency. Each outcome occurs with roughly equal probability or frequency.
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What is the shape of a distribution with two peaks called?
What is the shape of a distribution with two peaks called?
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Bimodal. Distribution has exactly two distinct peaks or modes.
Bimodal. Distribution has exactly two distinct peaks or modes.
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Identify the term for a data point significantly different from others.
Identify the term for a data point significantly different from others.
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Outlier. Values that fall unusually far from the typical data pattern.
Outlier. Values that fall unusually far from the typical data pattern.
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Find the mean of the data set: 2, 4, 6, 8.
Find the mean of the data set: 2, 4, 6, 8.
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- Sum is 20, divided by 4 observations gives mean of 5.
- Sum is 20, divided by 4 observations gives mean of 5.
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Choose the term that describes the peak of a distribution.
Choose the term that describes the peak of a distribution.
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Mode. The mode represents the highest point or most common value.
Mode. The mode represents the highest point or most common value.
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What is the mode of the data set: 4, 4, 5, 6, 7?
What is the mode of the data set: 4, 4, 5, 6, 7?
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- The value 4 appears most frequently in this data set.
- The value 4 appears most frequently in this data set.
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Calculate the range of the data set: 8, 3, 5, 12.
Calculate the range of the data set: 8, 3, 5, 12.
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- Maximum value (12) minus minimum value (3) equals 9.
- Maximum value (12) minus minimum value (3) equals 9.
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Which measure of spread is most resistant to outliers?
Which measure of spread is most resistant to outliers?
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Interquartile Range (IQR). IQR only uses middle 50% of data, ignoring extreme outliers.
Interquartile Range (IQR). IQR only uses middle 50% of data, ignoring extreme outliers.
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Find the median of the data set: 3, 5, 7, 9, 11.
Find the median of the data set: 3, 5, 7, 9, 11.
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- The middle value when 3, 5, 7, 9, 11 are arranged in order.
- The middle value when 3, 5, 7, 9, 11 are arranged in order.
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Identify the first step in creating a box plot.
Identify the first step in creating a box plot.
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Calculate the five-number summary. Min, Q1, median, Q3, and max are needed for the box plot structure.
Calculate the five-number summary. Min, Q1, median, Q3, and max are needed for the box plot structure.
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What is the term for the most frequent value in a data set?
What is the term for the most frequent value in a data set?
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Mode. The value that appears most often in the data set.
Mode. The value that appears most often in the data set.
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Which term describes a distribution with a longer left tail?
Which term describes a distribution with a longer left tail?
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Left-skewed. The tail extends toward lower values, creating negative skew.
Left-skewed. The tail extends toward lower values, creating negative skew.
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Which measure of center is affected by extreme values?
Which measure of center is affected by extreme values?
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Mean. Outliers pull the mean toward them, making it sensitive to extreme values.
Mean. Outliers pull the mean toward them, making it sensitive to extreme values.
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What is the definition of a quantitative variable?
What is the definition of a quantitative variable?
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A variable that can be measured numerically. Unlike categorical variables, these have numerical values that can be calculated.
A variable that can be measured numerically. Unlike categorical variables, these have numerical values that can be calculated.
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Identify the measure of center that is the middle value.
Identify the measure of center that is the middle value.
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Median. When data is ordered, this value sits exactly in the center position.
Median. When data is ordered, this value sits exactly in the center position.
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Find the range of the data set: 10, 15, 20, 25, 30.
Find the range of the data set: 10, 15, 20, 25, 30.
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- Maximum value (30) minus minimum value (10) equals 20.
- Maximum value (30) minus minimum value (10) equals 20.
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What is the term for the spread of data around the mean?
What is the term for the spread of data around the mean?
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Standard deviation. Square root of variance, measuring typical deviation from mean.
Standard deviation. Square root of variance, measuring typical deviation from mean.
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Which measure is used to describe the center of skewed data?
Which measure is used to describe the center of skewed data?
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Median. Median resists outlier influence better than mean in skewed data.
Median. Median resists outlier influence better than mean in skewed data.
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What does a box plot visually represent?
What does a box plot visually represent?
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The five-number summary. Box shows quartiles and whiskers extend to min/max values.
The five-number summary. Box shows quartiles and whiskers extend to min/max values.
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Identify one advantage of using a histogram.
Identify one advantage of using a histogram.
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Shows the shape of the data distribution. Visual pattern reveals skewness, modality, and spread characteristics.
Shows the shape of the data distribution. Visual pattern reveals skewness, modality, and spread characteristics.
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What is the purpose of a stem-and-leaf plot?
What is the purpose of a stem-and-leaf plot?
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To display data while retaining original values. Preserves actual data values unlike histograms that group data.
To display data while retaining original values. Preserves actual data values unlike histograms that group data.
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Which measure of center is affected by extreme values?
Which measure of center is affected by extreme values?
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Mean. Outliers pull the mean toward them, making it sensitive to extreme values.
Mean. Outliers pull the mean toward them, making it sensitive to extreme values.
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Which measure is used to describe the center of skewed data?
Which measure is used to describe the center of skewed data?
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Median. Median resists outlier influence better than mean in skewed data.
Median. Median resists outlier influence better than mean in skewed data.
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Find the mean of the data set: 2, 4, 6, 8.
Find the mean of the data set: 2, 4, 6, 8.
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- Sum is 20, divided by 4 observations gives mean of 5.
- Sum is 20, divided by 4 observations gives mean of 5.
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