Question

PLEASE HELP ME!!!!!
what is the upper and lower quartiles in this question:
58,59,60,62,64,67,68,69,70,73,74,75,75,76,78,81

Answer 1

Answer:

• Upper quartile = 75

• Lower quartile = 63

Step-by-step explanation:

We are given the following set of numbers:

58, 59, 60, 62, 64, 67, 68, 69, 70, 73, 74, 75, 75, 76, 78, 81.

We can see that there are 16 numbers in this set.

Since the numbers are already arranged in ascending order, we don't need to rearrange them.

Finding the upper quartile:

To find the position of the upper quartile of a set of numbers, we can use the formula:

$\boxed{Q_3 = \frac{3}{4}(n + 1)}$,

where:

• $Q_3$ = position of upper quartile

• $n$ = number of numbers in set (16).

Substituting $n = 16$ into the formula:

$Q_3 = \frac{3}{4}(16 + 1)$

    ⇒ $\frac{3}{4}(17)$

    ⇒ $\bf 12.75$

Since the position is a decimal number, we have to find the value above and below this position in the data set, and find their average. This means that, since our position is 12.75, we have to take the 12th and 13th values and find their mean.

∴ Upper quartile = $\frac{12th \space\ value \space\ + \space\ 13th \space\ value}{2}$

                            = $\frac{75+ 75}{2}$

                            = $\bf 75$

Finding the lower quartile:

To find the To find the position of the lower quartile of a set of numbers, we can use the formula:

$\boxed{Q_1 = \frac{1}{4}(n + 1)}$.

Substituting $n = 16$ into the formula:

$Q_3 = \frac{1}{4}(16 + 1)$

    ⇒ $\frac{1}{4}(17)$

    ⇒ $\bf 4.25$

As this is a decimal, we have to find the 4th and 5th values and calculate their average:

∴ Lower quartile = $\frac{4th \space\ value \space\ + \space\ 5th \space\ value}{2}$

                            = $\frac{62+ 64}{2}$

                            = $\bf 63$