Question

choose the correct description of the mean below
a. the mean is the sum of all the values divided by the number of values. it is not affected by outliers
b. the mean is the most common value in a data set. it can be strongly affected by outliers
c. the mean is the most common value in a data set. it is not affected by outliers
d. the mean is the sum of all the values divided by the number of values. it can be strongly affected by outliers
e. the mean is the middle value in a data set. it can be strongly affected by outliers
f. the mean is the middle value in a data set. it is not affected by outliers

choose the correct description of the median below
a. the median is the middle value in a data set. it can be strongly affected by outliers
b. the median is the middle value in a data set. it is not affected by outliers
c. the median is the sum of all the values divided by the number of values. it can be strongly affected by outliers
d. the median is the sum of all the values divided by the number of values. it is not affected by outliers
e. the median is the most common value in a data set. it is not affected by outliers
f. the median is the most common value in a data set. it can be strongly affected by outliers

Explanation:

For the mean question:

• Recall the definition of the mean: it's calculated as the sum of all values divided by the number of values. Also, the mean is sensitive to outliers (e.g., a very large or small value can pull the mean towards it).
• Option A says the mean is not affected by outliers (incorrect).
• Options B and C describe the mode (most common value), not the mean (incorrect).
• Option E and F describe the median (middle value), not the mean (incorrect).
• Option D correctly states the mean's calculation and its sensitivity to outliers.

For the median question:

• Recall the definition of the median: it's the middle value when data is ordered. The median is resistant to outliers (since it only depends on the middle position, not extreme values).
• Option A says the median is affected by outliers (incorrect).
• Options C and D describe the mean (sum divided by count), not the median (incorrect).
• Options E and F describe the mode (most common value), not the median (incorrect).
• Option B correctly states the median's definition and that it's not affected by outliers.

Answer:

Mean: D. The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers

Median: B. The median is the middle value in a data set. It is not affected by outliers