use the accompanying data set to complete the following actions.\na. find the quartiles.\nb. find the…

use the accompanying data set to complete the following actions.\na. find the quartiles.\nb. find the interquartile range.\nc. identify any outliers.\n61 60 55 56 63 59 60 58 63 63 61 61 60 56 75\na. find the quartiles.\nthe first quartile, q1, is \nthe second quartile, q2, is \nthe third quartile, q3, is \nb. find the interquartile range.\nthe interquartile range (iqr) is \nc. identify any outliers (use a commas to separate answers as needed) or type the letter b if there are no outliers.\nb. there are no outliers in the data set.

use the accompanying data set to complete the following actions.\na. find the quartiles.\nb. find the interquartile range.\nc. identify any outliers.\n61 60 55 56 63 59 60 58 63 63 61 61 60 56 75\na. find the quartiles.\nthe first quartile, q1, is \nthe second quartile, q2, is \nthe third quartile, q3, is \nb. find the interquartile range.\nthe interquartile range (iqr) is \nc. identify any outliers (use a commas to separate answers as needed) or type the letter b if there are no outliers.\nb. there are no outliers in the data set.

Answer

Explanation:

Step1: Sort the data

$55,56,56,56,58,59,60,60,60,61,61,61,61,63,63,63,75$

Step2: Find the median (Q2)

There are $n = 17$ data - points. The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{17+1}{2}=9$ - th value. So, $Q2=60$.

Step3: Find Q1

The lower - half of the data is $55,56,56,56,58,59,60,60$. There are $n_1 = 8$ data - points. The median of the lower - half is the $\frac{8 + 1}{2}=4.5$ - th value. So, $Q1=\frac{56 + 58}{2}=57$.

Step4: Find Q3

The upper - half of the data is $61,61,61,61,63,63,63,75$. There are $n_2 = 8$ data - points. The median of the upper - half is the $\frac{8+1}{2}=4.5$ - th value. So, $Q3=\frac{61 + 63}{2}=62$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=62 - 57 = 5$.

Step6: Identify outliers

Lower fence: $Q1-1.5\times IQR=57-1.5\times5=57 - 7.5 = 49.5$. Upper fence: $Q3 + 1.5\times IQR=62+1.5\times5=62 + 7.5 = 69.5$. The value $75$ is greater than $69.5$, so $75$ is an outlier.

Answer:

a. $Q1 = 57$, $Q2 = 60$, $Q3 = 62$ b. $IQR = 5$ c. $75$