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Marisa recorded the number of hours she babysat each day last summer. She plotted the data in the box plot. A number line goes from 0 to 7. The whiskers range from 2 to 7, and the box ranges from 3. 5 to 7. A line divides the box at 4. Which statement must be true according to the box plot? The data is symmetric and shows that she was equally likely to work more than 3. 5 hours or less than 5 hours. The data is symmetric and shows that she never worked more than 5 hours. The data is skewed and shows that she was equally likely to work more than 3. 5 hours or less than 5 hours. The data is skewed and shows that she never worked more than 5 hours.

Respuesta :

Box plot describes 5 important description of the data set it represents. The true statement according to the box plot specified is given by: Option C: The data is skewed and shows that she was equally likely to work more than 3. 5 hours or less than 5 hours.

How does a box plot shows the  data points?

A box plot has 5 data description.

  • The leftmost whisker shows the minimum value in the data.
  • The rightmost whisker shows the maximum value in the data.
  • The leftmost line in the box shows the first quartile.
  • The middle line shows the median, also called second quartile.
  • The last line of the box shows the third quartile.

How to find the interquartile range?

IQR(inter quartile range)  is the dfference between third and first quartile.

What is the range of a data set?

Range = Maximum value of the data set - Minimum value of the dataset

When is data symmetric for a given box plot?

Data is symmetric if the median is in the mid of the box plot and the box is mid to the line connecting both whiskers(since in that case, the frequencies are more likely to be distributed symmetric to the middle).

For the given case, it is described that:

Whiskers range from 2 and 7 thus, minimum of data set = 2, maximum value = 7

and the box ranges from 3. 5 to 7 (so first quartile is 3.5, and third quartile is at 7)

The line dividing box is at 4, thus, median or second quartile is 4.

Average of box's limit is (3.5 + 7)/2 = 5.25  

this is not coinciding with median, and actually lying ahead of median.

  • First quartile - min =  3.5-2 = 1.5
  • Third quartile - max = 7 - 7 = 0

That means data is leaning on right side(skewed negatively).

That means she worked more that median(the central measure here) thus, the data is skewed and shows that she was equally likely to work more than 3. 5 hours or less than 5 hours. (option C)

Learn more about box plot here:

https://brainly.com/question/1523909