Question

focus question: when is it appropriate to use the mean and median to summarize data? why?
it is best to use the mean when the shape of the distribution is ______________ because...

it is best to use the median when the shape of the distribution is ____________________ because...

Explanation:

for Mean:
The mean is affected by extreme values. In a symmetric (especially normal) distribution, data is evenly spread around the center, so the mean accurately represents the central tendency as it uses all data points and isn't skewed by outliers (since there are no extreme deviations in symmetric data).

for Median:
The median is resistant to outliers. In a skewed (left - skewed or right - skewed) distribution, extreme values (either very low in left - skewed or very high in right - skewed) pull the mean away from the center. The median, being the middle value, remains a better measure of the typical value as it isn't influenced by these extreme values.

Answer:

• It is best to use the mean when the shape of the distribution is symmetric (e.g., normal distribution) because the mean is a good measure of central tendency when data is evenly distributed around the center, and it is not affected by the lack of extreme values (outliers) that would skew it, as all data points are used in its calculation and the symmetric nature keeps it representative of the typical value.
• It is best to use the median when the shape of the distribution is skewed (left - skewed or right - skewed) because the median is resistant to outliers. In a skewed distribution, extreme values (either very low in left - skewed or very high in right - skewed) distort the mean, but the median, being the middle value, remains a more accurate representation of the typical value as it is not influenced by these extreme values.