Question

question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the new apartment building?
○ a
○ b
● c
○ d

question 2: which of the lines (a, b, c, or d) is most likely to be the median after including the new apartment building?
○ a
● b
○ c
○ d

question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply.
□ range
□ average
□ mode
□ median

question 4: in which of the cases should tewkesbury housing authority throw out or change the outlier? choose all that apply.
□ they will be adding another floor for more people onto the apartment building two years from now
□ it was registered incorrectly as an apartment building, but is actually 6 single - family homes constructed by the same builder
□ they are now building a new set of single - family homes further down the street
□ the apartment building was actually on the cross street, not on prentiss court

Explanation:

1. Question 1: The outlier (the new apartment building with ~9 people) pulls the mean toward it. The original data clusters around 2, so the mean will shift right from the original center, matching line C.
2. Question 2: The median is resistant to outliers. With most data clustered around 2, adding one outlier will not move the median far from the original central cluster, matching line B.
3. Question 3: Range depends on the minimum and maximum values, so outliers drastically increase it. The average (mean) is pulled toward outliers. Mode (most frequent value) and median (middle value) are not strongly affected by outliers.
4. Question 4: Outliers should only be removed if they are errors or do not belong to the dataset. A misclassified building (not an apartment) and a building on the wrong street do not belong to the target dataset. Future construction or new unrelated homes do not justify removing the existing outlier.

Answer:

1. C
2. B
3. Range, Average
4. It was registered incorrectly as an apartment building, but is actually 6 single-family homes constructed by the same builder; The apartment building was actually on the cross street, not on Prentiss Court