Answered

Which box-and-whisker plot represents the data set?


12, 10, 16, 19, 18, 14, 4, 18, 4




A box and whisker plot. The whiskers range from 4 to 19 and the box ranges from 5 to 12.5 with the vertical bar inside the box at 6.


A box and whisker plot. The whiskers range from 4 to 19 and the box ranges from 7 to 18 with the vertical bar inside the box at 14.


A box and whisker plot. The whiskers range from 4 to 19 and the box ranges from 5 to 14 with the vertical bar inside the box at 7.5.


A box and whisker plot. The whiskers range from 4 to 19 and the box ranges from 6 to 14 with the vertical bar inside the box at 10.

Verified Answer :

Answer:

A box and whisker plot. The whiskers range from 4 to 19 and the box ranges from 7 to 18 with the vertical bar inside the box at 14.

step-by-step-explanation:

We are given a set of data points by:

                      12, 10, 16, 19, 18, 14, 4, 18, 4

On arranging these data points in the increasing order or ascending order we get:

4, 4, 10, 12, 14, 16, 18, 18, 19.

Hence, based on the data points we have:

The range of the whisker plot is form 4-19

( Since the minimum value is 4 and the maximum value is 19)

The median of the data is the middle value of the data which is also known as the central tendency of the data .

Hence, the Median=14

Also, the lower set of data is:

        4, 4, 10, 12

so, the lower quartile lies between 4 and 10.

So, the lower quartile i.e.

\(Q_1=\dfrac{4+10}{2}\\\\Q_1=\dfrac{14}{2}\\\\Q_1=7\)

Hence, the start of the box is at 7.

Also, the upper set of data is:

          16 ,18, 18, 19.

So, the upper quartile lie between 18 and 18

Hence, the upper quartile i.e.

\(Q_3=18\)

Hence, the box range between 7 to 18.

Hence, the correct statement is:

A box and whisker plot. The whiskers range from 4 to 19 and the box ranges from 7 to 18 with the vertical bar inside the box at 14.

The whiskers range from 4 to 19 and the box ranges from 7 to 18 with the vertical bar inside the box at 14. Then the correct option is B.

What is a median?

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The data set is given as; 12, 10, 16, 19, 18, 14, 4, 18, 4

Arrange the data in the ascending order

4, 4, 10, 12, 14, 16, 18, 18, 19

14 is the middle term that can be treated as a median.

Median = 14

The lowest set of data

4, 4, 10, 12

The lower quartile lies between 4 and 10. Then Q₁ will be

\(\rm Q_1 = \dfrac{4+10}{2}\\\\Q_1 = \dfrac{14}{2}\\\\Q_1 = 7\)

Hence, the start of the box is at 7.

The upper set of data

16, 18, 18, 19

The lower quartile lies between 18 and 18. Then Q₃ will be

\(\rm Q_3= \dfrac{18+18}{2}\\\\Q_3= \dfrac{36}{2}\\\\Q_3= 18\)

Hence, the box range is between 7 and 18.

The whiskers range from 4 to 19 and the box ranges from 7 to 18 with the vertical bar inside the box at 14. Then the correct option is B.

More about the median link is given below.

https://brainly.com/question/300591

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