Question

mean: 514
median: 533
0 400 800 1200 1600 2000
number of customers
the next week, with the release of the blockbuster sequel, worst cops 4, the theater has 1960 customers.
0 400 800 1200 1600 2000
number of customers
question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the new sequel?
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 sequel?
a
b
c
d
question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply.
mode
median
range
average
question 4: in which of the cases should landmark cinema throw out or change the outlier? choose all that apply
the ticketing system that counted customers had a bug so that it counted too many customers
sequels are surefire ways of getting people to go to movies
by mistake, the person entering the data added a zero to the end of the number of customers when entering into the spreadsheet
the next 10 weeks had many fewer customers

Explanation:

Step1: Count original data points

Count the blue dots: 7 points.

Step2: Calculate new mean

Original sum: $514 \times 7 = 3598$. Add new value: $3598 + 1960 = 5558$. New count: $7+1=8$. New mean: $\frac{5558}{8}=694.75$

Step3: Identify new median position

Original median (7 points) is 4th value. New data (8 points) median is average of 4th and 5th values, both in original cluster near 533.

Step4: Recall outlier effects

Mean/average and range are affected by outliers; median/mode are not.

Step5: Identify valid outlier removal cases

Only remove outliers from measurement/data entry errors.

Answer:

Question 1: B
Question 2: A
Question 3:

• Range
• Average

Question 4:

• The ticketing system that counted customers had a bug so that it counted too many customers
• By mistake, the person entering the data added a zero to the end of the number of customers when entering into the spreadsheet