The $2009$ roster of the Dallas Cowboys professional football team included $10$ offensive linemen. Their weights (in pounds) were

Find the five-number summary for these data by hand. Show your work.

The minimum.

$Q_1$ (the first quartile, or the $25\%$ mark).

The median.

$Q_3$ (the third quartile, or the $25\%$mark).

The maximum.

In essence, five-number summaries provide rough facts.

No. of observations:$10$

Following the arrangement of the given data in ascending order:

$307,311,311,313,317,318,318,326,338,353$

To find the median, first sort the data in ascending order and use the middle numbers as the median.

So here median is $\frac{317+318}{2}=317.5$

Median: $317.5$

From the above-arranged data it is observed that the maximum: is $353$ and the minimum: is $317$

Now divides the list into two parts:

$307,311,311,313,317and318,318,326,338,353$

It's also simple to find the sub medians, which are the first and third quartiles because each half has five numbers.

So $Q_1=311$ and the minimum:$Q_3:326$

The following are five numerical summaries for the provided data:

1. The minimum: $317$

2. $Q_1=311$

3. The median: $317.5$

4. $Q_3=326$

5. The maximum: $353$