Comparing Data Sets: One Variable Statistics

What is the main difference between mean and median?

• Mean is used for categorical data, while median is used for numerical data.

• Mean is calculated by adding all values, while median is calculated by dividing the sum by the number of values.

• Mean is the average, while median is the middle value.

• Mean is the highest value, while median is the lowest value.

Answer explanation

Mean is the average, while median is the middle value.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Define range and interquartile range in the context of data sets.

• Range is max(data) - min(data) and Interquartile range is Q3 - Q1

• Range is mean(data) - median(data) and Interquartile range is Q3 - Q1

• Range is Q3 - Q1 and Interquartile range is max(data) - min(data)

• Range is Q3 - Q1 and Interquartile range is median(data) - mean(data)

Answer explanation

Range is calculated as max(data) - min(data) and Interquartile range is calculated as Q3 - Q1

Tags

CCSS.6.SP.B.5C

How do outliers and skewness affect the interpretation of data sets?

• Outliers can distort measures of central tendency and variability, while skewness affects the shape and symmetry of the data distribution.

• Skewness only affects measures of central tendency

• Outliers have no impact on data interpretation

• Outliers and skewness always improve data accuracy

Answer explanation

Outliers can distort measures of central tendency and variability, while skewness affects the shape and symmetry of the data distribution. This choice correctly explains how outliers and skewness impact data interpretation.

Explain how to interpret a box plot in terms of central tendency and spread.

• Measure the height of the box to identify outliers

• To interpret a box plot, look at the length of the box to understand the spread of the middle 50% of the data and the position of the median within the box to determine the central tendency. Check for outliers beyond the whiskers to identify extreme values.

• Look at the color of the box to determine central tendency

• Count the number of whiskers to understand spread

Answer explanation

To interpret a box plot, look at the length of the box to understand the spread of the middle 50% of the data and the position of the median within the box to determine the central tendency. Check for outliers beyond the whiskers to identify extreme values.

Tags

CCSS.6.SP.B.4

CCSS.HSS.ID.A.1

What insights can be gained from analyzing a histogram of a data set?

• Insights into historical events

• Insights into musical preferences

• Insights into weather patterns

• Insights into distribution, central tendency, variability, and outliers

Answer explanation

Analyzing a histogram provides insights into distribution, central tendency, variability, and outliers within a data set.

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CCSS.6.SP.A.3

Compare and contrast the measures of central tendency - mean, median, and mode.

• Mean is the average of all values, median is the middle value when the data is sorted, and mode is the value that appears most frequently.

• Median is the sum of all values divided by the number of values

• Mean is the highest value in the dataset

• Mode is the value that is closest to zero

Answer explanation

Answer Explanation highlighting the correct choice - Mean is the average of all values, median is the middle value when the data is sorted, and mode is the value that appears most frequently.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

What does the standard deviation indicate about the spread of data points in a data set?

• The standard deviation indicates the mode of data points in a data set.

• The standard deviation indicates the range of data points in a data set.

• The standard deviation indicates the median of data points in a data set.

• The standard deviation indicates the spread of data points around the mean.

Answer explanation

The standard deviation indicates the spread of data points around the mean.

When would you prefer to use the median over the mean in analyzing a data set?

• When the data set contains outliers or extreme values.

• When the data set has missing values

• When the data set is normally distributed

• When the data set has a small sample size

Answer explanation

The median is preferred over the mean when the data set contains outliers or extreme values to avoid skewing the results.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Calculate the range and interquartile range for the following data set: 10, 15, 20, 25, 30, 35, 40.

• Range: 5, Interquartile Range: 35

• Range: 45, Interquartile Range: 10

• Range: 25, Interquartile Range: 15

• Range: 30, Interquartile Range: 20

Answer explanation

The range is calculated by subtracting the smallest value (10) from the largest value (40), giving a range of 30. The interquartile range is the difference between the first quartile (15) and the third quartile (35), resulting in an interquartile range of 20.

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CCSS.6.SP.B.5C

Interpret the box plot below in terms of central tendency and spread: [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55]

• The central tendency is around the median value of 20, and the spread ranges from 10 to 50 with an interquartile range of 15 to 35.

• The central tendency is around the median value of 30, and the spread ranges from 5 to 55 with an interquartile range of 20 to 45.

• The central tendency is around the median value of 40, and the spread ranges from 15 to 45 with an interquartile range of 25 to 35.

• The central tendency is around the median value of 27.5, and the spread ranges from 5 to 55 with an interquartile range of 15 to 40.

Answer explanation

The central tendency is around the median value of 27.5, and the spread ranges from 5 to 55 with an interquartile range of 15 to 40.

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CCSS.7.SP.B.4