Question

descriptive statistics
the garden hotel analyzes the number of guests per week during the spring season.
here is the data for the first weeks of the season. each circle shows the number of guests in one week. the mean number of guests is 309 and the median number of guests is 318.
mean 309
median: 318
the next week, the analysis showed a large decrease in the number of people staying, with only 8 guests.
question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the next week’s data?
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 next week’s data?
a
b
c
d
question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply.
range
mode
median
average
question 4: in which of the cases should the garden hotel throw out or change the outlier? choose all that apply.
the decrease could have been due to street construction that reduced the amount of traffic
by mistake, the person entering data removed the last digit of the number of guests when entering into the spreadsheet
the number of guests at other hotels in the area did not show any decrease
the data was handwritten, and the person reading the data misread some digits

Explanation:

Step1: Count original data points

From the first dot plot, count the data points: 240, 280, 320, 320, 340, 360 → 6 points.

Step2: Calculate original total guests

Original mean = 309, so total = $309 \times 6 = 1854$.

Step3: Compute new mean with outlier

Add the new data point (8): new total = $1854 + 8 = 1862$, new n=7.
New mean = $\frac{1862}{7} \approx 266$. This is closest to line C.

Step4: Find new median with outlier

Ordered new data: 8, 240, 280, 320, 320, 340, 360. Median is the 4th value = 320, which is line D.

Step5: Identify outlier-sensitive stats

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

Step6: Determine valid outlier removal cases

Outliers are removed if data is erroneous (typo/misread) or confirmed invalid.

Answer:

Question 1: C
Question 2: D
Question 3: Range, Average
Question 4: By mistake, the person entering data removed the last digit of the number of guests when entering into the spreadsheet; The data was handwritten, and the person reading the data misread some digits