Question

use the accompanying data set to complete the following actions.
a. find the quartiles.
b. find the interquartile range.
c. identify any outliers.

41 52 36 43 42 38 40 46 45 38 36 56 42 35 15 53 38 49 29 30

a. find the quartiles.

the first quartile, \\(q_1\\), is \\(\box\\).
the second quartile, \\(q_2\\), is \\(\box\\).
the third quartile, \\(q_3\\), is \\(\box\\).
(type integers or decimals.)

Explanation:

Sort the dataset

Using the Median Calculation knowledge point

$$ \text{Data: } 41, 52, 36, 43, 42, 38, 40, 46, 45, 38, 36, 56, 42, 35, 15, 53, 38, 49, 29, 30 $$

$$ n = 20 $$

$$ \text{Sorted: } 15, 29, 30, 35, 36, 36, 38, 38, 38, 40, 41, 42, 42, 43, 45, 46, 49, 52, 53, 56 $$

Find the second quartile

Using the Median Calculation knowledge point

$$ Q_2 = \frac{\text{Value}_{10} + \text{Value}_{11}}{2} = \frac{40 + 41}{2} = 40.5 $$

Find the first quartile

Using the Percentiles and Quantiles knowledge point

$$ \text{Lower half (first 10 values): } 15, 29, 30, 35, 36, 36, 38, 38, 38, 40 $$

$$ Q_1 = \frac{\text{Value}_5 + \text{Value}_6}{2} = \frac{36 + 36}{2} = 36 $$

Find the third quartile

Using the Percentiles and Quantiles knowledge point

$$ \text{Upper half (last 10 values): } 41, 42, 42, 43, 45, 46, 49, 52, 53, 56 $$

$$ Q_3 = \frac{\text{Value}_{15} + \text{Value}_{16}}{2} = \frac{45 + 46}{2} = 45.5 $$

Answer:

a. Find the quartiles.

The first quartile, \(Q_1\), is <blank>36</blank>.
The second quartile, \(Q_2\), is <blank>40.5</blank>.
The third quartile, \(Q_3\), is <blank>45.5</blank>.
(Type integers or decimals.)