Question

summit high school analyzes the college test scores of its students each year on the rpt test. here is the data for this years students. each circle shows the test score of one student. the mean test score is 341 and the median test score is 332. mean: 341 median: 332 test score axis with data points a new student transferred in along with his score of 8 on the test, taken at another school new test score axis with lines a, b, c, d 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? options: 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? options: a, b, c, d question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply. options: median, average, range, mode question 4: in which of the cases should summit high school throw out or change the outlier? choose all that apply. options: by mistake, the other school sent the data for the wrong test; the data point doesnt matter as the student is not intending to go to college; the data was handwritten, and the person reading the data misread some digits; the new student had a bad cold on the day they took the test

Explanation:

Step1: Count original student number

Count the circles in the first plot: there are 7 students.

Step2: Calculate original total score

Original mean = 341, so total score: $7 \times 341 = 2387$

Step3: Calculate new total and mean

Add new score 8: $2387 + 8 = 2395$. New student count = 8. New mean: $\frac{2395}{8} = 299.375$

Step4: Analyze median change

Original median (7 students) is the 4th value = 332. New dataset (8 students) median is average of 4th and 5th values, both 332. New median: $\frac{332+332}{2}=332$

Step5: Identify outlier-sensitive stats

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

Step6: Validate outlier removal cases

Only errors in data collection/transmission justify removing an outlier.

Answer:

Question 1: C
Question 2: D
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