Question

The following stem-and-leaf plot represents the test scores for

Answer 1

Considering the given stem-and-leaf plot, the quartiles are given as follows:

• The first quartile is of 67.5.

• The second quartile, which is the median, is of 84.5.

• The third quartile is of 91.5.

What are the median and the quartiles of a data-set?

• The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

• The first quartile is the median of the first half of the data-set.

• The third quartile is the median of the second half of the data-set.

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:

Me = (83 + 86)/2 = 84.5.

The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:

Q3 = (91 + 92)/2 = 91.5.

More can be learned about the quartiles of a data-set at brainly.com/question/28017610

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