Question

the following data set shows the geometry test scores of students in a class: 78, 90, 87, 150, 95, 98, 82, 92, 85, 87. identify the outlier in this data set.

Explanation:

Step1: Arrange data in ascending order

78, 82, 85, 87, 87, 90, 92, 95, 98, 150

Step2: Find the median (Q2)

Since there are 10 data - points, the median is the average of the 5th and 6th ordered values. So, $Q2=\frac{87 + 90}{2}=88.5$.

Step3: Split data into lower and upper halves

Lower half: 78, 82, 85, 87, 87. Upper half: 90, 92, 95, 98, 150.

Step4: Find Q1 and Q3

For the lower half (5 data - points), the median (Q1) is the 3rd value, so $Q1 = 85$. For the upper half (5 data - points), the median (Q3) is the 3rd value, so $Q3=95$.

Step5: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1=95 - 85 = 10$.

Step6: Determine the lower and upper bounds for non - outliers

Lower bound: $Q1-1.5\times IQR=85-1.5\times10 = 70$. Upper bound: $Q3 + 1.5\times IQR=95+1.5\times10=110$.

Step7: Identify the outlier

Any value outside the range [70, 110] is an outlier. The value 150 is outside this range.

Answer:

150