here is a sample data set.\nfind the first quartile for this data set.\nq1=\nfind the third quartile for…

here is a sample data set.\nfind the first quartile for this data set.\nq1=\nfind the third quartile for this data set.\nq3=\nfind the inter - quartile range for this data set.\niqr=\nfind the lower fence separating outliers from usual values.\nfence_lower=\nfind the upper fence separating outliers from usual values.\nfence_upper=

here is a sample data set.\nfind the first quartile for this data set.\nq1=\nfind the third quartile for this data set.\nq3=\nfind the inter - quartile range for this data set.\niqr=\nfind the lower fence separating outliers from usual values.\nfence_lower=\nfind the upper fence separating outliers from usual values.\nfence_upper=

Answer

Explanation:

Step1: Count data points

There are 50 data - points in the data set.

Step2: Calculate position of first quartile ($Q_1$)

The position of $Q_1$ is $0.25\times(n + 1)$, where $n = 50$. So, $0.25\times(50+1)=12.75$. The first quartile is the value at the 12.75th position. Using interpolation, the 12th value is 306.5 and the 13th value is 313.4. $Q_1=306.5+(0.75)\times(313.4 - 306.5)=306.5 + 5.175=311.675$.

Step3: Calculate position of third quartile ($Q_3$)

The position of $Q_3$ is $0.75\times(n + 1)$. So, $0.75\times(50 + 1)=38.25$. The 38th value is 449.4 and the 39th value is 449.4. $Q_3=449.4+(0.25)\times(449.4 - 449.4)=449.4$.

Step4: Calculate inter - quartile range (IQR)

$IQR=Q_3 - Q_1=449.4-311.675 = 137.725$.

Step5: Calculate lower fence

Lower fence $=Q_1-1.5\times IQR=311.675-1.5\times137.725=311.675 - 206.5875=105.0875$.

Step6: Calculate upper fence

Upper fence $=Q_3 + 1.5\times IQR=449.4+1.5\times137.725=449.4+206.5875=655.9875$.

Answer:

$Q_1 = 311.675$ $Q_3 = 449.4$ $IQR = 137.725$ Lower fence $=105.0875$ Upper fence $=655.9875$