The box plots show Lauren's chemistry scores and her biology scores. Chemistry 2 box plots. The number line goes from 50 to 100.

Question

4 years ago

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The box plots show Lauren's chemistry scores and her biology scores. Chemistry 2 box plots. The number line goes from 50 to 100.

For chemistry, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80. For biology, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70. Biology Lauren used the steps below to determine the differences in the medians and the interquartile ranges. Step 1 Find the median for chemistry: 80 Find the median for biology: 70 Step 2 Find the difference in the medians: 80 minus 70 = 10 Step 3 Find the interquartile range for chemistry: 85 minus 80 = 5 Find the interquartile range for biology: 80 minus 70 = 10 Step 4 Find the difference in the interquartile ranges: 10 minus 5 = 5 Lauren determined that the difference in the medians is greater than the difference in the interquartile ranges. Which explains Lauren's error?

Mathematics

1 answer:

netineya [11] · Answer 1 · 2022-01-20T09:24:01+03:00

Answer:

<em>The error is in Step 3:</em>

She should have calculated the interquartile range as,

Chemistry = 85 - 60 = 25

Biology = 80 - 60 = 20

Step-by-step explanation:

*In a box plot, the median is the point on the number line where a line divides the rectangular box.

Thus, from the information given in the question about the box plots, the median for Chemistry = 80 (this is where a line divides the box)

Median for Biology = 70

The difference in the median = 80 - 70 = 10.

*Lauren didn't make any mistake in Step 1 and 2, as he equally got the same values.

==>The interquartile range in a box plot is simply the difference in the ranges (Q3 - Q1).

From the given information, the interquartile range for Chemistry = 85 - 60 = 25 (this is the difference in the ranges of the box)

Interquartile range for Biology = 80 - 60 = 20

The difference in interquartile range = 25 - 20 = 5

*Lauren made an error in Step 3 when calculating the interquartile range for both Chemistry and Biology, even though he arrive at the same value of the difference in the interquartile range we got as calculated above.