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 type your answer.\nthe second quartile, q2, is type your answer.\nthe third quartile, q3, is type your answer.\nb. find the inter - quartile range.\nthe interquartile range (iqr) is type your answer.\nc. identify any outliers (use a comma to separate answers as needed) or type the letter b if there are no outliers. type your answer.\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 type your answer.\nthe second quartile, q2, is type your answer.\nthe third quartile, q3, is type your answer.\nb. find the inter - quartile range.\nthe interquartile range (iqr) is type your answer.\nc. identify any outliers (use a comma to separate answers as needed) or type the letter b if there are no outliers. type your answer.\nb. there are no outliers in the data set.

Answer

Explanation:

Step1: Sort the data

$51,55,56,56,58,59,60,60,60,61,61,61,63,63,75$

Step2: Find the median (Q2)

There are $n = 15$ data - points. The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{15+1}{2}=8$-th value, so $Q2 = 60$.

Step3: Find Q1

The lower - half of the data is $51,55,56,56,58,59,60$. There are $n_1=7$ data - points. The median of the lower - half is the $\left(\frac{7 + 1}{2}\right)$-th value, so $Q1 = 56$.

Step4: Find Q3

The upper - half of the data is $60,61,61,61,63,63,75$. There are $n_2 = 7$ data - points. The median of the upper - half is the $\left(\frac{7+1}{2}\right)$-th value, so $Q3 = 61$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=61 - 56 = 5$.

Step6: Identify outliers

The lower fence is $Q1-1.5\times IQR=56-1.5\times5=56 - 7.5 = 48.5$. The upper fence is $Q3 + 1.5\times IQR=61+1.5\times5=61 + 7.5 = 68.5$. The value $75$ is greater than $68.5$, so $75$ is an outlier.

Answer:

a. The first quartile, Q1, is $56$. The second quartile, Q2, is $60$. The third quartile, Q3, is $61$. b. The interquartile range (IQR) is $5$. c. $75$