# Atlanta had the following temperatures recorded for the last nine days of February: 44, 49, 39, 43, 50, 44, 45, 49, 51 For this data, which summary statistic in NOT correct?

## The minimum is 39. The lower quartile (Q1) is 44. The median is 45. The maximum is 51.

Aug 26, 2017

#### Answer:

See a solution process below:

#### Explanation:

Minimum Temperature

To find the minimum we can write the temperatures in sorted order:

$39 , 43 , 44 , 44 , 45 , 49 , 49 , 50 , 51$

The minimum is indeed 39. This IS correct!

Maximum Temperature

Looking at the sorted order again, the maximum is indeed 51. This IS correct!

Median Temperature

The Median is the "middle" value of a sorted set of numbers.

$39 , 43 , 44 , 44 , \textcolor{red}{45} , 49 , 49 , 50 , 51$

In this problem the median is indeed 45. This IS correct!

Lower Quartile

We can rewrite the sorted temperatures as:

$\left(39 , \textcolor{b l u e}{43} , \textcolor{b l u e}{44} , 44\right) , \textcolor{red}{45} , 49 , 49 , 50 , 51$

The lower quartile (Q1) is the median of the lower half of the numbers (the temperatures in parenthesis).

Because there is an even number of temperatures in the bottom half we need to add the two middle numbers and divide by $2$:

$\frac{\textcolor{b l u e}{43} + \textcolor{b l u e}{44}}{2} = \frac{87}{2} = 43.5$

44 is NOT Q1. This is NOT correct!