Respuesta :
You can use the given data to find the 5 information box plot needs to make and use the construction rule for box plot to select the best box plot among given options.
The box plot best representing the given observations is
Option B: Box plot with minimum value 9. 1, lower quartile 9. 2, median 9. 4, upper quartile 9. 7, and maximum value 9. 8
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 inter-quartile range?
IQR(inter quartile range) is the difference between third and first quartile.
Using the above fact and the data given to chose the best box plot among the given box plots
The given data is
9.4, 9.2, 9.7, 9.8, 9.4, 9.7, 9.6, 9.3, 9.2, 9.1, 9.4
The sorted data in ascending order is
9.1, 9.2, 9.2, 9.3, 9.4, 9.4, 9.4, 9.6, 9.7, 9.7, 9.8
The mid value(6th here since there are 11 observations) is the median = 9.4
The minimum value is 9.1
The maximum value is 9.8
The first quartile is the average of the two mid values of the first 6 observation(it is because 6 is even, otherwise we'd've taken mid value)
It is (3rd value + 4th value)/2 = 9.25
The third quartile is the average of the two mid value of the last 6 observations.
It is (8th value + 9th value)/2 = (9.6 + 9.7)/2 = 9.65
The second option is best representing the given information compared to other options.
Thus,
The box plot best representing the given observations is
Option B: Box plot with minimum value 9. 1, lower quartile 9. 2, median 9. 4, upper quartile 9. 7, and maximum value 9. 8
Learn more about box plot here:
https://brainly.com/question/1523909
