Question

The following box and whiskers plot represents the number of passengers travelling in a bus at different times of a day.


Which of the following is correct for the above box and whiskers plot?

• A.

  Lower extreme	$95$
  Upper extreme	$130$
  Lower quartile	$65$
  Middle quartile	$110$
  Upper quartile	$145$
  Inter-quartile range	$35$

• B.

  Lower extreme	$65$
  Upper extreme	$145$
  Lower quartile	$95$
  Middle quartile	$110$
  Upper quartile	$130$
  Inter-quartile range	$35$

• C. None of the above.

Answer 1

The correct option is B

Lower extreme	$65$
Upper extreme	$145$
Lower quartile	$95$
Middle quartile	$110$
Upper quartile	$130$
Inter-quartile range	$35$

Let's infer the extremes and quartiles for the following box and whiskers plot one by one.


$\bullet$ Lower extreme is the left-most data point, i.e., the left end point of lower whisker.
$\therefore$ Lower extreme= $65$

$\bullet$ Upper extreme is the right-most data point, i.e., the right end point of upper whisker.
$\therefore$ Upper extreme= $145$

$\bullet$ Lower quartile is the left edge data point of the box.
$\therefore$ Lower quartile= $95$

$\bullet$ Middle quartile is represented by the vertical mark inside the box.
$\therefore$ Middle quartile= $110$

$\bullet$ Upper quartile is the right edge data point of the box.
$\therefore$ Upper quartile= $130$

$\bullet$ Inter-quartile range is given by the difference between the upper and lower quartiles.

$\therefore \text{Inter-quartile range= Upper quartile - Lower quartile}$
$\Rightarrow \text{Inter-quartile range}=130-95$
$\Rightarrow \text{Inter-quartile range}=35$

Therefore, option (b.) is the correct one.

$\underset{–}{\text{Observations:}}$

$\bullet$ The length of lower whisker is greater than the length of upper whisker. Hence, the lower (first) $25\%$ of data are more spreaded than the upper (last) $25\%$ of data.

$\bullet$ In the box, the length of left part of middle quartile is less than the length of right part of middle quartile. Hence, lower $25\%$ of data in the box are more clumped as compare to upper $25\%$ of data in the box.