Question

Which statements about the box plot are correct? Check all that apply.

Fifty percent of the data values lies between 34 and 46.
Seventy-five percent of the data values lies between 42 and 70.
It is unlikely that there are any outliers.
The interquartile range'is 24.
The range is 36

Answer 1

A,C

Explanation:

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Answer 2

The correct options are 1 and 3.

Explanation:

From the given box plot it is clear that

`\text{Minimum values}=34`

`Q_1=42`

Q₁ is 25% of a data.

`Median=46`

Median is 50% of a data.

`Q_3=70`

Q₃ is 75% of a data.

`\text{Maximum values}=76`

34 is minimum value of the data and 46 is median it means 50% of the data values lies between 34 and 46. Therefore option 1 is correct.

42 is first quartile and and 70 is third quartile. it means 50% of the data values lies between 42 and 70. Therefore option 2 is incorrect.

The difference between Minimum value and first quartile, Maximum value and third quartile is less than 1.5×(IQR), therefore it is unlikely to have any outliers in the data.

Hence option 3 is correct.

The interquartile range of the data is

`IQR=Q_3-Q_1`

`IQR=70-42=28`

The interquartile range is 28. Therefore option 4 is incorrect.

Range of the data is

`Range=Maximum-Minimum`

`Range=76-34=42`

The range is 42. Therefore option 5 is incorrect.