Question

representing data
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?
mean
median
both mean and median
neither mean nor median

Explanation:

Step1: Calculate the mean

First, sum all the scores: \(60 + 62 + 67 + 69 + 70 + 70 + 71 + 75 + 76 + 120\). Let's compute that: \(60+62 = 122\), \(122+67 = 189\), \(189+69 = 258\), \(258+70 = 328\), \(328+70 = 398\), \(398+71 = 469\), \(469+75 = 544\), \(544+76 = 620\), \(620+120 = 740\). Then divide by the number of scores (10): \(\frac{740}{10}=74\).

Step2: Calculate the median

Since there are 10 scores (even number), the median is the average of the 5th and 6th values. The scores in order are: 60, 62, 67, 69, 70, 70, 71, 75, 76, 120. The 5th value is 70, the 6th is 70. So median is \(\frac{70 + 70}{2}=70\).

Step3: Determine best measure

The mean is 74, but there's an outlier (120) which pulls the mean up. The median (70) is less affected by the outlier and better represents the central tendency of most scores (most are around 70, except 120).

Answer:

The mean test score total is \(74\).
The median test score total is \(70\).
Which measure of center best represents the test data? median