Question

question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the single family home?
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 single family home?
a
b
c
d

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

question 4: in which of the cases should platteville housing office throw out or change the outlier? choose all that apply:
they will be remodeling the home to house more people in the next two years
they are now building a new, much larger apartment building further down the street
it was registered incorrectly as a single - family home, but is actually a row of townhouses that holds 15 people
the single - family home was actually on the cross street, not on young avenue

Explanation:

1. Question 1: The mean is strongly pulled toward outliers. A single-family home (likely an outlier with lower occupancy than multi-unit buildings) would shift the mean toward the lower end, so line C (the leftmost shifted value) is correct.
2. Question 2: The median is resistant to outliers; adding one outlier will only minimally shift it or keep it near the original central value, so line D (closest to the original median) is correct.
3. Question 3: The average (mean) uses all data points, so outliers skew it heavily. The range is calculated as max - min, so an outlier will drastically alter this value. The median and mode are not strongly affected by outliers.
4. Question 4: Outliers should be corrected/removed only if they are data entry errors or do not belong to the dataset. Incorrect registration and wrong location are valid reasons to adjust/remove the outlier. Future remodeling or new construction do not affect the current data's validity.

Answer:

1. Question 1: C
2. Question 2: D
3. Question 3: Average, Range
4. Question 4:

• It was registered incorrectly as a single-family home, but is actually a row of townhouses that holds 15 people
• The single-family home was actually on the cross street, not on Young Avenue