Question

descriptive statistics
part 2 of 2
centennial high school analyzes the college test scores of its students each year on the drp test.
here is the data for this years students. each circle shows the test score of one student. the mean test score is 356 and the median test score is 365.
mean: 356
median: 365
a new student transferred in along with his score of 8 on the test, taken at another school.
question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the new student?
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 student?
a
b
c
d
question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply.
average
mode
median
range
question 4: in which of the cases should centennial high school throw out or change the outlier? choose all that apply.
the data point doesnt matter as the student is not intending to go to college
by mistake, the other school sent the data for the wrong test
the new student had a bad cold on the day they took the test
the data was handwritten, and the person reading the data misread some digits

Explanation:

Step1: Count original data points

Count the circles: $n_1 = 8$

Step2: Calculate original total score

Total = Mean $\times n_1 = 356 \times 8 = 2848$

Step3: Update total and sample size

New total = $2848 + 8 = 2856$; New $n_2 = 8 + 1 = 9$

Step4: Compute new mean

New mean = $\frac{2856}{9} \approx 317.33$

Step5: Find new median position

Median position = $\frac{9+1}{2} = 5$th value (sorted data)

Step6: Identify median from sorted data

Sorted data: 8, 300, 320, 340, 360, 360, 380, 380, 400. 5th value = 360

Step7: Recall outlier effects

Mean (average) and range are sensitive to outliers; median/mode are not.

Step8: Evaluate outlier removal criteria

Only remove outliers if data is invalid (wrong test, misread digits).

Answer:

Question 1: B
Question 2: C
Question 3:

• Average
• Range

Question 4:

• By mistake, the other school sent the data for the wrong test
• The data was handwritten, and the person reading the data misread some digits