Question

The frequency table summarizes the distribution of time that $140$patients at the

emergency room of a small-city hospital waited to receive medical attention during the

last month.

Waiting time	Frequency
Less than $10$minutes	$5$
At least $10$ but less than $20$ minutes	$24$
At least $20$ but less than $30$ minutes	$45$
At least $30$ but less than $40$ minutes	$38$
At least $40$ but less than $50$ minutes	$19$
At least $50$ but less than $60$ minutes	$7$
At least $60$ but less than $70$ minutes	$2$

Which of the following represents possible values for the median and IQR of waiting

times for the emergency room last month?

a. median = $27$minutes and IQR = $15$minutes

b. median = $28$minutes and IQR = $25$minutes

c. median = $31$minutes and IQR = $35$minutes

d. median = $35$minutes and IQR = $45$minutes

e. median = $45$minutes and IQR = $55$minutes

Short answer

Option (a) median = $27$and IQR=$15$ is Correct.

Step-by-step solution

Given Information

We have to select the best option from the multiple choice question according to the given question.

Waiting time	Frequency
Less than$10$minutes	$5$
At least $10$ but less than $20$ minutes	$24$
At least $20$ but less than $30$ minutes	$45$
At least $30$but less than $40$ minutes	$38$
At least$40$but less than $50$minutes	$19$
At least$50$ but less than$60$ minutes	$7$
At least $60$ but less than $70$ minutes	$2$

Explanation

Let's start with the total frequency:

$5+24+45+38+19+7+2=140$

The average of the $70$th and $71$st values will be the median.

Because the first two categories have a frequency of $5+24=29$and the first three categories have a frequency of $5+24+45=74$, the $70$th and $71$st values will fall into the third group, and the median will be between $20$and $30$minutes.

We also know that the distribution is right skewed, which means that the mean is greater than the median. Therefore, correct option is (b).