Question

The graph below represents the distribution of scores on a placement test for students at Central High School. Select the statement that is true about the distribution of scores.

Placement Test Results


a.

The mode is the greater than the median.

c.

The mode is less than the median.

b.

There are two medians

d.

The median and mode are the same.




Please select the best answer from the choices provided

Answer 1

A- The mode is the greater than the median

Step-by-step explanation:

Answer 2

Answer: Choice A) The mode is greater than the median

Mode = 95, median = 90

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Step-by-step explanation:

The mode is the most frequent value. In this case, the mode is 95. All we do is look for the highest bar, and then record the x value connected with it. The higher the bar, the more frequent the value.

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The median will take a bit more work, but it's not too bad.

First add up the heights of every bar shown:

2+3+4+6+7+10+5 = 37

So there are 37 scores. The median will be in the very exact middle. Divide 37 over 2 to get 37/2 = 18.5

Erase off the 0.5 and we can say that 18 values are below the median, and 18 values are above the median. So we have 18+1+18 = 37 values total.

The median will be in slot 18+1 = 19.

From here, we add up the bar heights (starting on the left and working toward the right). We're trying to see when we reach 19 or higher, since the median is in that 19th slot.

• Add the first two bar heights: 2+3 = 5. That value is not 19 or larger.
• Add the first three bar heights: 2+3+4 = 9. Still not 19 or larger
• First four bar heights: 2+3+4+6 = 15. We're getting closer, but still no.
• First five bars: 2+3+4+6+7 = 22. We've crossed over 19. The median must be 90 because that x value is tied to the fifth bar.

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To summarize:

• mode = 95
• median = 90

The mode is larger than the median.

This is why choice A is the answer.