GMAT statistics strategies

The mean is the sum of the values divided by the count: $\text{mean} = \frac{\sum x_i}{n}$. The median is the middle value when the numbers are sorted (or the average of the two middle values if the count is even). The mode is the most frequent value. Standard deviation measures how far the values spread from the mean. The GMAT rarely asks you to compute standard deviation by hand, but it does test how adding or removing a value changes it.

Adding a value equal to the mean leaves the mean unchanged. Adding a value above the mean raises it, and adding one below lowers it. The median is more resistant: for a set with an odd count, the median shifts by at most one position. For the set 2, 4, 6, 8, 10, the mean is 6 and the median is 6. Add a 100: the mean jumps to $\frac{130}{6} \approx 21.7$, but the median only moves to 7 (the average of 6 and 8). The mean is sensitive to outliers, the median is not. The GMAT tests this distinction directly.

The salaries of 5 employees are $40,000, $45,000, $50,000, $55,000, and $200,000. What is the difference between the mean and the median? Step 1: Identify the measures. The question asks for both the mean and the median, then the difference. Step 2: Compute the mean. The sum is $40 + 45 + 50 + 55 + 200 = 390$ thousand. Divide by 5: the mean is $78,000. Step 3: Compute the median. The values are already sorted. With 5 values, the median is the third one, which is $50,000. Step 4: Find the difference. The mean minus the median is $78 - 50 = 28$ thousand. The answer is $28,000. The outlier at $200,000 pulls the mean far above the median.