Exploring Measures of Central Tendency and Dispersion

What does the interquartile range (IQR) measure in a data set?

• The total spread of the data

• The difference between the mean and mode

• The average of all data points

• The range between the first and third quartiles

What is the primary use of a box and whisker plot in data analysis?

• To determine the mode

• To show the distribution of data

• To calculate the mean

• To compute the variance

How is variance calculated in a data set?

• By summing the squares of the differences from the mean

• By finding the average of all data points

• By dividing the range by the number of data points

• By multiplying the mean by the number of data points

What does a higher standard deviation indicate about a data set?

• Data points are more spread out from the mean

• Data points do not vary

• Data points are closer to the mean

• Data points are less frequent

Which statistical measure will not change when all data points are increased by a constant?

• Standard deviation

• Median

• Mode

• Mean

How does subtracting a constant from every data point affect the standard deviation?

• It decreases

• It resets to zero

• It remains unchanged

• It increases

What statistical values are calculated directly from a graphing calculator in the tutorial?

• Standard deviation and variance only

• Mean and median only

• Mode, median, and range only

• Mode, mean, median, range, IQR, variance, and standard deviation

What effect does multiplying all data points by a negative number have on the mean?

• The mean becomes zero

• The mean becomes negative

• The mean doubles

• There is no change to the mean

If every data point in a set is multiplied by 2, what happens to the variance?

• It quadruples

• It doubles

• It remains the same

• It halves

What is the effect of data transformation by addition on the mean of a data set?

• The mean increases by the same amount added

• The mean is reset to zero

• The mean is unchanged

• The mean decreases