Center, Shape, & Spread of Data - ACT Math
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What does a positively skewed distribution indicate?
What does a positively skewed distribution indicate?
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Tail on the right side is longer; mean > median. Right-skewed with outliers pulling mean up.
Tail on the right side is longer; mean > median. Right-skewed with outliers pulling mean up.
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Identify the mode of the data set: 2, 2, 3, 4, 5.
Identify the mode of the data set: 2, 2, 3, 4, 5.
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Mode = 2. Value 2 appears twice, most frequent.
Mode = 2. Value 2 appears twice, most frequent.
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How do you calculate the range of a data set?
How do you calculate the range of a data set?
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Subtract the smallest value from the largest value. Difference between maximum and minimum values.
Subtract the smallest value from the largest value. Difference between maximum and minimum values.
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Which measure describes the variability of a data set?
Which measure describes the variability of a data set?
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Standard deviation. Measures how spread out data points are.
Standard deviation. Measures how spread out data points are.
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What is the median of the data set: 3, 5, 7, 9, 11?
What is the median of the data set: 3, 5, 7, 9, 11?
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- Middle value when arranged in order.
- Middle value when arranged in order.
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What is the formula for the mean of a data set?
What is the formula for the mean of a data set?
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Mean = $\frac{\text{sum of all data points}}{\text{number of data points}}$. Add all values and divide by count.
Mean = $\frac{\text{sum of all data points}}{\text{number of data points}}$. Add all values and divide by count.
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How is the shape of a data set described?
How is the shape of a data set described?
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Using terms like symmetric, skewed left, skewed right. Describes distribution pattern and tail direction.
Using terms like symmetric, skewed left, skewed right. Describes distribution pattern and tail direction.
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What is the formula for the standard deviation?
What is the formula for the standard deviation?
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Standard deviation = $\sqrt{\text{variance}}$. Square root of the variance value.
Standard deviation = $\sqrt{\text{variance}}$. Square root of the variance value.
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State the formula for the range of a data set.
State the formula for the range of a data set.
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Range = $\text{max value} - \text{min value}$. Difference between highest and lowest values.
Range = $\text{max value} - \text{min value}$. Difference between highest and lowest values.
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Find the range of the data set: 2, 4, 6, 8.
Find the range of the data set: 2, 4, 6, 8.
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Range = 6. Maximum 8 minus minimum 2 equals 6.
Range = 6. Maximum 8 minus minimum 2 equals 6.
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Identify the mode of the data set: 3, 3, 6, 9, 9, 12.
Identify the mode of the data set: 3, 3, 6, 9, 9, 12.
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Modes = 3 and 9. Both 3 and 9 appear twice.
Modes = 3 and 9. Both 3 and 9 appear twice.
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Find the standard deviation of the data set: 4, 4, 4, 4.
Find the standard deviation of the data set: 4, 4, 4, 4.
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Standard deviation = 0. No variation means zero spread.
Standard deviation = 0. No variation means zero spread.
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What is the median of the data set: 3, 5, 7, 9, 11?
What is the median of the data set: 3, 5, 7, 9, 11?
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- Middle value when arranged in order.
- Middle value when arranged in order.
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Identify the skewness of the data: 1, 2, 3, 4, 10.
Identify the skewness of the data: 1, 2, 3, 4, 10.
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Skewed right. Outlier 10 creates long right tail.
Skewed right. Outlier 10 creates long right tail.
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Calculate the mean for the data: 5, 10, 15.
Calculate the mean for the data: 5, 10, 15.
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Mean = 10. Sum (30) divided by count (3).
Mean = 10. Sum (30) divided by count (3).
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Find the standard deviation of the data set: 4, 4, 4, 4.
Find the standard deviation of the data set: 4, 4, 4, 4.
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Standard deviation = 0. No variation means zero spread.
Standard deviation = 0. No variation means zero spread.
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What is a characteristic of a symmetric distribution?
What is a characteristic of a symmetric distribution?
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Mean and median are approximately equal. No skew means balanced distribution.
Mean and median are approximately equal. No skew means balanced distribution.
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What is the mean of the data set: 2, 4, 6, 8, 10?
What is the mean of the data set: 2, 4, 6, 8, 10?
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Mean = 6. Sum (30) divided by count (5).
Mean = 6. Sum (30) divided by count (5).
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What does the standard deviation measure in a data set?
What does the standard deviation measure in a data set?
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It measures the spread of data around the mean. Shows how far values deviate from average.
It measures the spread of data around the mean. Shows how far values deviate from average.
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How do you find the mode of a data set?
How do you find the mode of a data set?
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Mode is the number that appears most frequently. Look for the value with highest frequency.
Mode is the number that appears most frequently. Look for the value with highest frequency.
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Calculate the range for the data: 9, 13, 21, 28.
Calculate the range for the data: 9, 13, 21, 28.
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Range = 28 - 9 = 19. Largest minus smallest value.
Range = 28 - 9 = 19. Largest minus smallest value.
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What is the formula for finding the z-score?
What is the formula for finding the z-score?
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z = $\frac{x - \text{mean}}{\text{standard deviation}}$. Standardizes values relative to distribution.
z = $\frac{x - \text{mean}}{\text{standard deviation}}$. Standardizes values relative to distribution.
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What does a histogram display?
What does a histogram display?
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Frequency distribution of a data set. Shows how often values occur in intervals.
Frequency distribution of a data set. Shows how often values occur in intervals.
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What is a box plot used for?
What is a box plot used for?
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Visualizing the distribution, center, and spread of data. Shows five-number summary graphically.
Visualizing the distribution, center, and spread of data. Shows five-number summary graphically.
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Which measure of central tendency is least affected by outliers?
Which measure of central tendency is least affected by outliers?
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Median. Outliers don't affect middle position value.
Median. Outliers don't affect middle position value.
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What is the effect of an outlier on the mean?
What is the effect of an outlier on the mean?
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An outlier can significantly affect the mean. Extreme values pull the average away.
An outlier can significantly affect the mean. Extreme values pull the average away.
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State the formula for variance of a data set.
State the formula for variance of a data set.
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Variance = $\frac{\text{sum of squared deviations from mean}}{n}$. Measures average squared distance from mean.
Variance = $\frac{\text{sum of squared deviations from mean}}{n}$. Measures average squared distance from mean.
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Identify the range of the data set: 4, 8, 15, 16, 23, 42.
Identify the range of the data set: 4, 8, 15, 16, 23, 42.
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Range = 42 - 4 = 38. Subtract minimum from maximum value.
Range = 42 - 4 = 38. Subtract minimum from maximum value.
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What is the interquartile range (IQR)?
What is the interquartile range (IQR)?
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IQR = Q3 - Q1, difference between third and first quartiles. Measures spread of middle 50% of data.
IQR = Q3 - Q1, difference between third and first quartiles. Measures spread of middle 50% of data.
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Identify the mode of the data set: 3, 3, 6, 9, 9, 12.
Identify the mode of the data set: 3, 3, 6, 9, 9, 12.
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Modes = 3 and 9. Both 3 and 9 appear twice.
Modes = 3 and 9. Both 3 and 9 appear twice.
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