Question

descriptive statistics
part 2 of 2 1 2 trying to earn
tewkesbury housing authority analyzes the number of people per building on every street.
here is the data for prentiss court in 2023, which has only single - family homes. each circle shows the number of people in one building. the mean number of people is 2.2 and the median number of people is 2.3.
mean: 2.2
median: 2.3
0 2 4 6 8 10
number of people
in 2024, a new apartment building is built on prentiss court with 9 people.
0 2 4 6 8 10
number of people
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:

Step1: Count original data points

From the first dot plot, count the circles: there are 10 data points (each circle is a building).

Step2: Calculate original total people

Original mean = 2.2, so total people = $10 \times 2.2 = 22$

Step3: Calculate new total and mean

Add 9 people, new total = $22 + 9 = 31$, new $n=11$. New mean = $\frac{31}{11} \approx 2.82$, which is closest to line B.

Step4: Find original median position

Original $n=10$, median is average of 5th and 6th values, both 2, so median 2.3 (given, confirms ordered data: most values 2, some slightly higher).

Step5: Find new median position

New $n=11$, median is the 6th value, which is still 2, matching line A.

Step6: Recall outlier sensitivity

Mean (Average) and Range are affected by outliers; Median/Mode are not.

Step7: Identify valid outlier removal cases

Outliers are removed if data is misclassified or belongs to a different group.

Answer:

Question 1: B
Question 2: A
Question 3: Range, Average
Question 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