The following stem-and-leaf plot represents the test scores for
26 students in a class on their most recent test. Use the data provided to find the quartiles.
Stem
Leaves
6 0 1 2 2 4 7 8
7 0 1 2 5 8
8 3 6 6 7 9 9
9 0 1 2 2 2 4 5 8
Key:
6|0=60

To find the second quartile, we must first divide the data in half. There are an even number of data values, so the 50th percentile, or median, is the arithmetic mean of the two values in the middle of the set. Thus, the median is the mean of the 13th data value,
83 and the 14th data value, 86
83+86/2=84.5
Therefore, the second quartile is 84.5
Step 2 of 3 : Find the first quartile.

Question

16-07-2022
Mathematics

contestada

The following stem-and-leaf plot represents the test scores for
26 students in a class on their most recent test. Use the data provided to find the quartiles.
Stem
Leaves
6 0 1 2 2 4 7 8
7 0 1 2 5 8
8 3 6 6 7 9 9
9 0 1 2 2 2 4 5 8
Key:
6|0=60

To find the second quartile, we must first divide the data in half. There are an even number of data values, so the 50th percentile, or median, is the arithmetic mean of the two values in the middle of the set. Thus, the median is the mean of the 13th data value,
83 and the 14th data value, 86
83+86/2=84.5
Therefore, the second quartile is 84.5
Step 2 of 3 : Find the first quartile.

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joaobezerra joaobezerra · Answer 1 · 2022-07-18T20:25:19+02:00

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 https://brainly.com/question/28017610

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