Question

Given the following stem-and-leaf plot and the statements shown below the plot, which of the statements are true?
The number of customers in line for an attraction
$2|222247$
$3|1223567$
$4|577$
$5|0111$
Where $3|6$ means $36$ customers
I. The mode is equal to the median
II. The median is less than the mean
III. The mean is $33$

• A. I only
• B. II only
• C. III only
• D. I and II only
• E. None of the above

Answer 1

The correct option is B II only

$\Rightarrow$ The number of customers in line are $22,22,22,22,24,27,31,32,32,33,35,36,37,45,47,47,50,51,51,51$.

$\Rightarrow$ $Mean=\frac{22+22+22+22+24+27+31+32+32+35+36+37+45+47+47+50+51+51+51}{20}$

$=\frac{768}{20}=38.4$

$\Rightarrow$ Here, $n$ is even number which is $20$

$Median={(\frac{n}{2}+1)}^{th}observation={(\frac{20}{2}+1)}^{th}observation={11}^{th}observation$

$\therefore$ $Median=35$

$\Rightarrow$ Here, $22$ occurs $4$ times which is maximum.

$\therefore$ $Mode=22$

$\Rightarrow$ So, here we can see only statement $II$ is true. The median is less than the mean.