GMAT Focus Edition — Data Insights: Table Analysis · Graphics Interpretation · Multi-Source Reasoning · Two-Part Analysis
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Data Insights Lesson 18 of 20

Lesson 18:
Averages & Weighted Logic in Data Sets

Apply the weighted average formula in DI data contexts. Distinguish simple average from weighted average and use the sum trick.

⏱ 50 mins
🎯 DI 75 to 88
📚 Prereq: Lesson 12 (Statistics in Quant)
Note: Lesson 18 of 20 — Averages & Weighted Logic in Data Sets.
1

Core Concepts: Averages & Weighted Logic in Data Sets

Apply the weighted average formula in DI data contexts. Distinguish simple average from weighted average and use the sum trick.

Key Framework
Weighted avg = total sum / total count
Add all individual values, divide by total count. Never average averages.
Sum = Mean × n
Use this to recover the total sum from the group's mean and count.
Weighted mean pulls toward the larger group
The combined average is always between the two group averages, closer to the larger group.
Median requires sorting
Mean and median differ when outliers are present. Know which is asked.
2

Application Strategy

Step-by-Step Approach
①
Identify the question type and the specific metric being asked about.
②
Locate the relevant data in the chart, table, or tab.
③
Apply the key formula or logic rule from the framework above.
④
Verify that your answer satisfies the question as stated.
3

Visual Reference Diagram

Visual Framework for Lesson 18
📊
Weighted avg = total sum / total count
📈
Sum = Mean × n
🔍
Weighted mean pulls toward the larger group
📋
Median requires sorting
4

Quick Reference Rules

▸
Weighted avg = total sum / total count: Add all individual values, divide by total count. Never average averages.
▸
Sum = Mean × n: Use this to recover the total sum from the group's mean and count.
▸
Weighted mean pulls toward the larger group: The combined average is always between the two group averages, closer to the larger group.
▸
Median requires sorting: Mean and median differ when outliers are present. Know which is asked.
5

10 Traps for Lesson 18

⚠ Confusing the key formula for this topic

Review the core rule: Weighted avg = total sum / total count

⚠ Reading the wrong data series

Always verify axis labels and legends before extracting values.

⚠ Ignoring units or scale

Check units on every axis before computing ratios or changes.

⚠ Treating estimates as exact

GI data requires interpolation — use approximate values and pick the closest answer.

⚠ Forgetting the denominator

Sum = Mean × n — always identify what you're dividing by.

⚠ Applying simple average when weighted is needed

If group sizes differ, compute weighted average, not simple mean.

⚠ "All" statements need every row verified

One counterexample makes a universal statement False.

⚠ Scope: data sample ≠ full population

Conclusions are limited to the data range provided, not broader populations.

⚠ Confusing absolute and relative measures

Absolute change ($) and relative change (%) answer different questions.

⚠ Not using the complement when helpful

P(at least one) = 1 − P(none). In set logic, use complement for "not" conditions.

✦

10 Practice Questions

Q1 of 10
GI~700

Group A: 20 people, avg score 80. Group B: 30 people, avg score 90. Combined average = ?

Explanation: 86. Total = 20×80 + 30×90 = 1600+2700 = 4300. Combined avg = 4300/50 = 86.
Q2 of 10
GI~600

The average of 5 numbers is 40. A sixth number (70) is added. New average = ?

Explanation: 45. Sum of 5 = 200. New sum = 270. New avg = 270/6 = 45.
Q3 of 10
GI~550

The median of {3, 7, 9, 12, 15} is:

Explanation: 9. Sorted set (already sorted). Middle value of 5 elements = 3rd element = 9.
Q4 of 10
GI~650

If each value in a set is multiplied by 3, the standard deviation:

Explanation: Triples. When all values are multiplied by a constant k, SD multiplies by |k|. Multiplying by 3 → SD × 3.
Q5 of 10
GI~650

Set A = {10, 20, 30, 40, 50}. Adding constant 5 to all values: new mean and SD are:

Explanation: Mean+5, SD unchanged. Adding a constant shifts the mean but leaves SD (which measures spread) unchanged.
Q6 of 10
GI~700

A data set has mean 50, SD 10. What percentage of a normal distribution falls within ±1 SD (i.e., between 40 and 60)?

Explanation: 68%. The empirical rule: approximately 68% of data falls within ±1 SD of the mean in a normal distribution. ±2 SD = 95%. ±3 SD = 99.7%.
Q7 of 10
GI~650

A weighted average is being computed for exam scores. Midterm (weight 30%) = 70; Final (weight 70%) = 90. Weighted avg = ?

Explanation: 84. 0.30×70 + 0.70×90 = 21+63 = 84.
Q8 of 10
GI~700

The average of a list of 8 numbers is 25. If 2 numbers (30 and 20) are removed, new average = ?

Explanation: 25. Original sum = 8×25 = 200. Removed sum = 30+20 = 50. New sum = 150. New avg = 150/6 = 25. The removed values averaged to 25 (= the mean), so mean is unchanged.
Q9 of 10
GI~600

A table shows test scores for 3 classes. Which class had the highest average?

Explanation: The class with total/n closest to 100. Average = total/count. To find the highest average, divide each class's total score by its student count and compare.
Q10 of 10
GI~700

5 consecutive even integers have a mean of 14. The smallest is:

Explanation: 10. Consecutive even integers: n, n+2, n+4, n+6, n+8. Mean = n+4 = 14 → n = 10.
Lesson Summary
Weighted avg = total sum / total count

Add all individual values, divide by total count. Never average averages.

Sum = Mean × n

Use this to recover the total sum from the group's mean and count.

Weighted mean pulls toward the larger group

The combined average is always between the two group averages, closer to the larger group.

Median requires sorting

Mean and median differ when outliers are present. Know which is asked.

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