Question

6,7,8,9, 11, 13, 14, 14, 18
Q1: ?Q3:?

Answer 1

`Q_1` = 7.5

`Q_3` = 14

Explanation:

We are given the following data;

6, 7, 8, 9, 11, 13, 14, 14, 18

Now,
`Q_1` is called the first Quartile of the data which represents the 25% of the data values.

`Q_3` is called the third Quartile of the data which represents the 75% of the data values.

Now, calculation of quartiles;

• 
  `Q_1` is given by =
  `((n+1)/(4))^(th)` obs. {where n = 9}

=
`((9+1)/(4))^(th)` obs

=
`((10)/(4))^(th)` obs =
`2.5^(th)` obs

So,
`Q_1` =
`2^(nd)` obs + 0.5(
`3^(rd)` -
`2^(nd)`)

= 7 + 0.5(8-7) = 7 + 0.5 = 7.5

• 
  `Q_3` is given by =
  `3Q_1` =
  `3((n+1)/(4))^(th)` obs. {where n = 9}

=
`3((9+1)/(4))^(th)` obs

=
`3((10)/(4))^(th)` obs =
`(3 * 2.5)^(th)` obs =
`7.5^(th)` obs.

So,
`Q_3` =
`7^(th)` obs + 0.5(
`8^(th)` -
`7^(th)`)

= 14 + 0.5(14 - 14) = 14 + 0 = 14

Therefore,
`Q_1` = 7.5 and
`Q_3` = 14.

Answer 2

Answer: Q1 = 7.5

Q3 = 14

Explanation:

Q1 means the lower quartile of a group of numbers and Q3 means the upper quartile. Once the median of such group of numbers are established then the the median of the lower set of numbers is the Q1 and the median of the upper set of numbers is the Q3.

We're given the data:

6,7,8,9, 11, 13, 14, 14, 18

Median of the general set of numbers = 11.

Q1= median of 6,7,8,9 = (7+8)/2 = 7.5

Q3 = median of 13,14,14,18 = (14+14)/2 = 14