the following numbers of people attended the last 10 screenings of a movie. 117, 195, 196, 202, 203, 206…

Explanation:

Step1: Arrange data in ascending order

117, 195, 196, 202, 203, 206, 207, 211, 211, 296

Step2: Find the median (Q2)

Since there are 10 data - points, the median is the average of the 5th and 6th ordered values. $Q2=\frac{203 + 206}{2}=204.5$

Step3: Find the lower half and its median (Q1)

The lower half is 117, 195, 196, 202, 203. The median of the lower half $Q1 = 196$

Step4: Find the upper half and its median (Q3)

The upper half is 206, 207, 211, 211, 296. The median of the upper half $Q3=211$

Step5: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1=211 - 196 = 15$

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

Lower bound: $Q1-1.5\times IQR=196-1.5\times15=196 - 22.5 = 173.5$ Upper bound: $Q3 + 1.5\times IQR=211+1.5\times15=211 + 22.5 = 233.5$

Step7: Identify outliers

Values less than 173.5 or greater than 233.5 are outliers. So the outlier is 296

Answer:

296