Question

for the following distribution, decide whether you expect the mean, median, or mode to give the best representation of the center of the distribution, and explain why.

the individual weights of oranges in a 5-pound bag.

choose the correct answer below.

a. the mean because it is the most commonly understood measure of center.
b. the mean because there are likely to be few outliers.
c. the median because it is easier to calculate.
d. the mode because it will find the most common weight(s).
e. the mode because there are likely to be outliers.
f. the median because there are likely to be outliers.

Explanation:

Analyze the distribution characteristics

We are looking at the individual weights of oranges in a 5-pound bag. Oranges packaged together in a standard bag are sorted by size and weight to meet packaging standards. Because of this commercial sorting, the weights of these oranges will be very similar to one another, clustering closely around a central average weight.

Evaluate the presence of outliers

Since the oranges are pre-sorted to fit standard packaging, it is highly unlikely that a bag would contain an extremely tiny orange or a massive, giant orange. Therefore, the distribution of individual weights is expected to be symmetric and free of extreme values, meaning there are likely to be few outliers.

Determine the best measure of center

Using the Measures of Center concept, when a dataset is symmetric and has few or no outliers, the mean is the most reliable and preferred measure of center because it incorporates every data point in the calculation without being distorted by extreme values. If there were significant outliers, the median would be preferred instead.

Match with the given options

Since we expect a symmetric distribution with few outliers, the mean is the best representation of the center. This directly corresponds to option B: "The mean because there are likely to be few outliers."

Answer:

• (A) The mean because it is the most commonly understood measure of center.
• (B) The mean because there are likely to be few outliers. (Correct answer)
• (C) The median because it is easier to calculate.
• (D) The mode because it will find the most common weight(s).
• (E) The mode because there are likely to be outliers.
• (F) The median because there are likely to be outliers.