Question

PLZZZZZZZZZZ HELP

Which data set is represented by the modified box plot? Box and whisker plot on a number line from 40 to 120 in increments of 5. The whisker ranges from 66 to 85. The box ranges from 68 to 82 with the vertical bar inside the box at 75. One dot mark above forty-six. One dot mark above one hundred and eight.
A.85, 78, 80, 108, 46, 66, 68, 82, 72, 68
B.85, 70, 80, 108, 46, 66, 68, 82, 70, 68
C.85, 78, 80, 108, 46, 66, 68, 82, 72, 80
D.85, 78, 80, 108, 46, 66, 68, 80, 72, 68

Answer 1

Option A.

Explanation:

It is given that the whisker ranges from 66 to 85. It means the minimum value of the data is 66 and maximum value is 85.

The box ranges from 68 to 82 with the vertical bar inside the box at 75. It means Q₁=68, Median=75 and Q₃=82.

One dot mark above forty-six. One dot mark above one hundred and eight.

First data set is

85, 78, 80, 108, 46, 66, 68, 82, 72, 68

Arrange the data in ascending order.

46, 66, 68, 68, 72, 78, 80, 82, 85, 108

Divide the data in four equal parts.

(46, 66), 68,( 68, 72), (78, 80), 82,( 85, 108)

`Q_1=68`

`Median=(72+78)/(2)=75`

`Q_3=82`

Option A is correct.

Similarly,

The second data set

(46, 66), 68,( 68, 70), (70, 80), 82, (85, 108)

`Q_1=68`

`Median=(70+70)/(2)=70\\eq 75`

`Q_3=82`

Option B is incorrect.

The third data set

(46, 66), 68,( 72, 78), (80, 80), 82, (85, 108)

`Q_1=68`

`Median=(78+80)/(2)=79\\eq 75`

`Q_3=82`

Option C is incorrect.

The fourth data set

(46, 66), 68,( 68, 72), (78, 80), 80, (85, 108)

`Q_1=68`

`Median=(72+78)/(2)=75`

`Q_3=80\\eq 82`

Option D is incorrect.

Therefore, the correct option is A.

Answer 2

The correct answer is: Option: A

A. 85, 78, 80, 108, 46, 66, 68, 82, 72, 68

Explanation:

It is given that:

The whisker ranges from 66 to 85.

The box ranges from 68 to 82 with the vertical bar inside the box at 75.

• Hence, the minimum value of the box plot is: 66

• Maximum value of box plot is: 85

Also,

• The first quartile or the lower quartile i.e.
  `Q_1` is: 68

• The middle quartile or median i.e.
  `Q_2` is: 75

• The upper quartile or third quartile i.e.
  `Q_3` is: 82

Also, it is given that:

One dot mark above forty-six.

One dot mark above one hundred and eight.

A)

On arranging the data in increasing order after removing outliers 46 and 108 we have:

66 68 68 72 78 80 82 85

Hence, from this data we have:

Minimum value=66

maximum value=85

`Q_1=68\\\\Q_2=75\\\\\\Q_3=81`

As all the values matches the value defined.

Hence, this option is correct.

B)

On arranging the data in increasing order after removing 46 and 108 we have:

66 68 68 70 70 80 82 85

Hence, from this data we have:

Minimum value=66

maximum value=85

`Q_1=68\\\\Q_2=70\\\\\\Q_3=81`

As the value of
`Q_2=70\\eq 75`.

Hence, this option is incorrect.

C)

On arranging the data in increasing order after removing 46 and 108 we have:

66 68 72 78 80 80 82 85

Hence, from this data we have:

Minimum value=66

maximum value=85

`Q_1=70\\\\Q_2=79\\\\\\Q_3=81`

As the value of
`Q_1,Q_2\ and Q_3` do not match.

Hence, this option is incorrect.

D)

On arranging the data in increasing order after removing 46 and 108 we have:

66 68 68 72 78 80 80 85

Hence, from this data we have:

Minimum value=66

maximum value=85

`Q_1=68\\\\Q_2=79\\\\\\Q_3=80`

As the value of
`Q_3=80\\eq 82` do not match.

Hence, this option is incorrect.