7th grade math i.4 worksheet 1\n1) find the outlier of the data set.\n43, 69, 49, 78, 88, 54, 73, 194, 54…
7th grade math i.4 worksheet 1\n1) find the outlier of the data set.\n43, 69, 49, 78, 88, 54, 73, 194, 54, 59, 70
Answer
Explanation:
Step1: Sort the data set
$43,49,54,54,59,69,70,73,78,88,194$
Step2: Find the median (Q2)
There are 11 data - points. The median is the 6th value. So, $Q2 = 69$.
Step3: Find the lower half and its median (Q1)
The lower half is $43,49,54,54,59$. The median of the lower half (Q1) is 54.
Step4: Find the upper half and its median (Q3)
The upper half is $70,73,78,88,194$. The median of the upper half (Q3) is 78.
Step5: Calculate the inter - quartile range (IQR)
$IQR=Q3 - Q1=78 - 54 = 24$.
Step6: Calculate the lower and upper bounds for non - outliers
Lower bound: $Q1-1.5\times IQR=54-1.5\times24=54 - 36 = 18$. Upper bound: $Q3 + 1.5\times IQR=78+1.5\times24=78 + 36 = 114$.
Step7: Identify the outlier
Any value less than 18 or greater than 114 is an outlier. The outlier in the data set is 194.
Answer:
194