Q 2.1. - The Practice of Statistics for AP

Question

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. 

Step-by-Step Solution

Answer

1. The minimum: $317$

2. ${Q }_1= 311$

3. The median: $317.5$

4. ${Q }_3= 326$

5. The maximum: $353$

Step 1: Given information

Step 2: Concept

The minimum.

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

The median.

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

The maximum.

Step 3: Calculation

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:

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

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: $353$