Question

Plot the box and whiskers graph for the following data, and comment on the spreadness of the given data set.

$52$

$54$

$56$

$68$

$54$

$78$

$97$

$34$

$22$

$65$

$82$

• A.
  Comment: $2^{\text{nd}}$ $25$% of the data points are tightly clamped.
• B.
  Comment: $3^{\text{rd}}$ $25$% of the data points are tightly clamped.

Answer 1

The correct option is A

Comment: $2^{\text{nd}}$ $25$% of the data points are tightly clamped.
After arranging the given data set in ascending order, we get:

$\underset{–}{22}$

$34$

$\underset{–}{52}$

$54$

$54$

$\underset{–}{56}$

$65$

$68$

$\underset{–}{78}$

$82$

$\underset{–}{97}$

The total number of data points in the given data set is $11$.

$\bullet \text{Middle value = Median = Middle quartile}$
$\therefore$ Middle quartile = $56$

$\bullet$ Lower quartile= Median of $\{22,34,52,54,54\}$= $52$
$\bullet$ Upper quaritle= Median of $\{65,68,78,82,97\}$= $78$

The lower, middle and upper quartiles segregate the data points into four equal intervals.

And,
$\bullet$ Lower extreme= $22$
$\bullet$ Upper extreme= $97$

$\therefore$ The box and whiskers plot of the given data set is


In the above box and whiskers plot,
$\bullet$ Cyan points: Lower and upper extremes ($22,97$)
$\bullet$ Orange points: Lower and upper quartiles ($52,78$)
$\bullet$ Green point: Middle quartile ($56$)

Here, we observe that the second $25\%$ of the data points are tightly clumped than the rest of the quarters, i.e., option (a.) is the correct one.