Question:medium
The incidence of malaria in an area is 20, 20, 50, 56, 60, 5000, 678, 898, 345, 456. Which of these methods is the best to calculate the average incidence?
The incidence of malaria in an area is 20, 20, 50, 56, 60, 5000, 678, 898, 345, 456. Which of these methods is the best to calculate the average incidence?
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One extreme value (5000) skews this data badly; the median resists outliers far better than the arithmetic mean does.
Updated On: Jul 8, 2026
- Arithmetic mean
- Geometric mean
- Median
- Mode
Show Solution
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Whenever one number in a data set is wildly bigger than the rest, as 5000 is here compared to values like 20, 50, or 60, that one number can badly distort a plain average.
Step 2: See what the outlier does to the mean.
The arithmetic mean adds every value and divides by the count, so the huge 5000 gets baked directly into that sum and pulls the mean well above where most of the data actually clusters. That makes the mean a poor stand-in for typical incidence here.
Step 3: Rule out mode and geometric mean too.
The mode fails outright since no value in the list repeats. The geometric mean is built for growth rates and ratios, not raw incidence counts, and can still be dragged by the same extreme value, so it is not the natural fit here.
Step 4: See why the median survives the outlier.
The median only cares about position after sorting, not about size. Whether the largest value is 5000 or 50,000 makes no difference to where the middle of the list falls, so it stays a fair representative of the typical incidence.
Step 5: Final Answer:
Because it resists distortion from the single extreme value, the median is the best method to calculate the average incidence.
Whenever one number in a data set is wildly bigger than the rest, as 5000 is here compared to values like 20, 50, or 60, that one number can badly distort a plain average.
Step 2: See what the outlier does to the mean.
The arithmetic mean adds every value and divides by the count, so the huge 5000 gets baked directly into that sum and pulls the mean well above where most of the data actually clusters. That makes the mean a poor stand-in for typical incidence here.
Step 3: Rule out mode and geometric mean too.
The mode fails outright since no value in the list repeats. The geometric mean is built for growth rates and ratios, not raw incidence counts, and can still be dragged by the same extreme value, so it is not the natural fit here.
Step 4: See why the median survives the outlier.
The median only cares about position after sorting, not about size. Whether the largest value is 5000 or 50,000 makes no difference to where the middle of the list falls, so it stays a fair representative of the typical incidence.
Step 5: Final Answer:
Because it resists distortion from the single extreme value, the median is the best method to calculate the average incidence.
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