Question

c. the outlier in league a (28 goals) was recorded incorrectly - it should be 18. which measures will change more significantly: mean/median or standard deviation/iqr? explain.

Explanation:

Step1: Understand the effect of outliers on measures

The mean is the sum of all values divided by the number of values. An outlier can greatly affect the sum and thus the mean. The median is the middle - value when data is ordered. It is less affected by outliers as it only depends on the position in the ordered data set. The standard deviation measures the spread of data around the mean, so it is also affected by outliers as they increase the spread. The inter - quartile range (IQR) is the difference between the third and first quartiles and is resistant to outliers as it focuses on the middle 50% of the data.

Step2: Analyze the change when outlier is corrected

When the outlier (28 goals) is corrected to 18 goals, the sum of the data values will change. Since the mean is based on the sum, it will change significantly. The median may or may not change depending on the number of data points and their original order. The standard deviation will change as the spread of data around the mean will be different. The IQR is less likely to change as it does not depend on extreme values.

Answer:

The mean will change more significantly.