Question

Use the list below to find the upper quartile. 27, 5, 11, 13, 10, 8, 14, 18, 7

Answer 1

Answer:

The upper quartile is 7.5.                                          

Step-by-step explanation:

Given : Data - 27, 5, 11, 13, 10, 8, 14, 18, 7

To find : The upper quartile of the data ?

Solution :

Arrange the data from least to greatest,

5, 7, 8, 10, 11, 13, 14, 18, 27

First we find the median of the data.

As number of terms 9 is odd the median is $\frac{n+1}{2}$ th term,

$\frac{n+1}{2}=\frac{9+1}{2}=5$th term

The 5th term of data is median is 11.

Before 11 is the data range of upper quartile.

i.e. data - 5, 7, 8, 10

Now, The upper quartile is the median of the upper quartile range.

Median of even term is given by, $\frac{1}{2}(\frac{n}{2}th+\frac{n}{2}+1)th$

$\frac{1}{2}(\frac{4}{2}th+\frac{4}{2}+1)th=\frac{1}{2}(2nd+3rd)$

$m=\frac{1}{2}(7+8)$

$m=\frac{1}{2}(15)$

$m=7.5$

The upper quartile is 7.5.

Answer 2

Find the  median first. The middle of all the numbers.

5, 7, 8, 10, 11, 13, 14, 18, 27

11 is the median.

Then find the median of the upper quartile.

The upper quartile consists of numbers...

5, 7, 8, 10

Since it is an even set of numbers add the two in the middle and divided by two. So 7 plus 8=  15/2.

7.5 is your upper quartile.