Body Temperature. A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6°F$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6°F$the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich' (Journal of the American Medical Association, Vol. data-custom-editor="chemistry" $268$, pp. $1578-1580$) Among other data, the researchers obtained the body temperatures of $93$healthy humans, as provided on the Weiss Stats site

We are given that,

Sorted data is given in the Weiss stats which are as follows,

$$\begin{gathered} 96.7,96.8,96.9,97,97,97,97,97.1,97.2,97.2,97.2,97.3,97.3,97.4, \\ 97.4,97.4,97.4,97.4,97.4,97.6,97.6,97.6,97.6,97.7,97.7,97.7, \\ 97.8,97.8,97.8,97.8,97.9,98,98,98,98,98,98,98,98,98,98,98, \\ 98.1,98.1,98.1,98.2,98.2,98.2,98.2,98.2,98.2,98.2,98.2,98.3, \\ 98.3,98.4,98.4,98.4,98.4,98.4,98.4,98.5,98.5,98.5,98.5,98.6, \\ 98.6,98.6,98.6,98.6,98.6,98.6,98.6,98.6,98.7,98.7,98.8,98.8, \\ 98.8,98.8,98.8,98.8,98.8,99,99,99,99,99.1,99.2,99.2,99.3, \\ 99.3,99.4 \end{gathered}$$

As we know that median is the middle value of a sorted data set. Since the number of data values is odd, the median is:-

$Q_2=98.2$

So, roughly $50\%$the states have percentage of adults in required condition is below$98.2°F$

Now, the first quartile is the median of values below $Q_2$i.e.

$Q_1=97.65$

So, roughly $25\%$the states have percentage of adults in required condition is below $97.65°F$

Now, the third quartile is the median of values below localid="1650920063246" $Q_2$

$Q_3=98.6$

So, roughly $75\%$the states have percentage of adults in required condition is below $98.6°F$

We need to find out the interquartile range

The interquartile range is the difference between $Q_1$and$Q_3$

$IQR=Q_3-Q_1=98.6-97.65=0.95$

The middle $50\%$of the healthy humans have body temperature varies by$0.95°F$

We need to find out the five-number summary

The five-number summary is minimum$=96.7$, first quartile$=97.65$, second quartile$=98.2$, third quartile$=98.6$ and maximum$=99.4$

We need to find out the potential outliers.

An outlier is more than $1.5IQR$or greater than $Q_3$or less than $Q_1$

Therefore,

$$\begin{gathered} Q_3+\left(1.5IQR\right)=98.6+\left(1.5\times 0.95\right)=100.025 \\ {Q}_3-\left(1.5IQR\right)=97.65-\left(1.5\times 0.95\right)=97.175 \end{gathered}$$

Hence, $49$is outlier because it is not in range of outliers

We need to find the boxplot which is given below

The whiskers of the boxplot are at a low and high value. The box starts at $Q_1$and ends at $Q_3$and has a straight line at the median.