Question

7th grade math i.4 worksheet 1

1. find the outlier of the data set.

43, 69, 49, 78, 88, 54, 73, 194, 54, 59, 70

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