Question

The earnings per share of a stock during a 7-month period: $4.2, $5.05, $5.6, $5.9, $6.5, $7.2, and $4.4Find the three quartiles of the data.

Answer 1

The question gives us earnings per share over a 7 month period and we are asked to find the 3 quartiles of the data.

In order to do this, we will first need to arrange the data in ascending order.

This is done below:

`\begin{gathered} 4.2,5.05,5.6,5.9,6.5,7.2,4.4 \\ \text{ Rearrange in ascending order} \\ \\ 4.2,4.4,5.05,5.6,5.9,6.5,7.2 \end{gathered}`

Now, assign a rank to each number from left to right:

`\begin{gathered} 4.2\to\text{ 1st} \\ 4.4\to\text{ 2nd} \\ 5.05\to\text{ 3rd} \\ \vdots \\ 7.2\to\text{ 7th} \end{gathered}`

Now, we can apply the Quartile formula to find the first, second and third quartiles.

The Quartile formula is given below:

`\begin{gathered} Q_i=\mleft((i(n+1)/(4)\mright)^(th) \\ i=1,2,3\text{ (for quartile one, two or three)} \\ n=\text{ Number of data points given. In this case, there are } \\ 7\text{ earnings we were given, hence we have 7 data points} \end{gathered}`

This formula gives the position of the quartiles.

After getting the number we need, this number represents the position of the quartile in the re-arranged data above.

Now let us find the quartiles

First Quartile (Q1):

`\begin{gathered} Q_i=((i(n+1)/(4))^(th) \\ i=1\text{ (First quartile}),n=7 \\ Q_1=\mleft((1*(7+1))/(4)\mright)^(nd) \\ \\ \therefore Q_1=((8)/(4))^(nd)=2^(nd) \end{gathered}`

Hence, the first quartile Q1 is in the second position.

Counting from left to right from the re-arranged data:

4.2, 4.4, 5.05, 5.6, 5.9, 6.5, 7.2

Thus, Q1 = 4.4

Second Quartile:

Using the same formula;