Question

Math 18 12:30 pm Summer 2018 Homework: Section 2.5 Measure Position Score: 0 of 1 pt 2.5.13 Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 42 50 36 45 41 36 39 47 45 38 36 54 43 35 15 52 38 49 29 30 a. Find the quartiles. The first quartile, Q,, is The second quartlie, Q2, is The third quartle, Os, is Type integers or decimals.)

Answer 1

First arrange data in ascending order.

15	29	30	35	36	36	36	38	38	39
41	42	43	45	45	47	49	50	52	54

The first quartile is the middle value/average of two middle values of the lowest half data. Therefore:

$Q_1=\frac{36+36}{2}={\color{Red} 36}$

The second quartile is the middle value/average of two middle values of the whole data. Therefore:

$Q_2=\frac{39+41}{2}={\color{Red} 40}$

The third quartile is the middle value/average of two middle values of the greatest half data. Therefore:

$Q_3=\frac{45+47}{2}={\color{Red} 46}$

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The interquartile range is:

$IQR=Q_3-Q_1=46-36={\color{Red} 10}$

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Lower and upper limits are:

$\\Lower \ limit=Q_1-1.5IQR=36-1.5(10)=21 \\Upper \ limit=Q_3+1.5IQR=46+1.5(10)=61$

Any data value below 21 or greater than 61 is considered as an outlier. In the dataset, 15 is below 21.

Therefore:

$outlier={\color{Red} 15}$