Question

Some of Mrs. Turay’s eighth graders took the PSAT test. Score totals of ten of her students are below. Calculate the mean and the median, and determine which provides a better view of the score data. Scores: 60, 62, 67, 69, 70, 70, 71, 75, 76, 120 The mean test score total is . The median test score total is . Which measure of center best represents the test data?

Answer 1

Mean is 74

Median is 70

The best measure of center is the Median.

Answer 2

Answer:

(a) Mean=74

(b) Median=70

(c) The best measure of center= Median.

Step-by-step explanation:

We have been given a data set of PSAT scores of Mrs. Turay's eight graders. We are asked to find mean and median of the given data set.

(a) Let us find mean of data set by dividing the sum of given scores by the number of students.

$\text{Mean}=\frac{60+62+67+69+70+70+71+75+76+120}{10}$

$\text{Mean}=\frac{740}{10}=74$

Therefore, the mean test score will be 74.

(b) Now let us find median of our given data set. We have been given that number of students is 10, therefore, our median will be the average of 5th and 6th term.

60, 62, 67, 69, 70, 70, 71, 75, 76, 120.

We can see that 5th term is 70 and 6th term is 70 as well.

$\text{Median}=\frac{70+70}{2}$

$\text{Median}=\frac{140}{2}$

$\text{Median}=70$

Therefore, the median test scores will be 70.

(c) We can see that our data set has an outlier score as 120, which has increased the mean. Mean score is greater than median score. Since median is not affected by extreme value outliers, therefore, median will be the best measure of center for given test scores.