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Lesson: Applied Arithmetic - 20t01

In-Format Mean, Median, Mode, And Range Problems

[Page 20 of 36]
Task Now let's try some in-format problems. Click on the correct response and then click Continue.

A bowler bowls five games and scores 140, 120, 175, 140, and 195 on those games. Which of the following is true of these scores?

I.    The median is higher than the mode.
II.The average (arithmetic mean) is higher than the median.
III. The range is less than half the average (arithmetic mean).

None
III only
I and II
II and III
I, II, and III

Continue

For starters, rearrange the scores in ascending order: 120, 140, 140, 175, 195.

The resulting middle number, 140, is the median, and since 140 is the only recurring number, it is also the mode. Thus Statement I is incorrect and Choices (3) and (5) are out.

To evaluate Statement II, we're going to have to calculate the average:

So (1) and (2) are out, and (4) must be the answer.

(But just to prove that Statement III works, the range = 195 - 120 = 75, which is less than half the average, which we know is 154.)

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