Free Guide: Average Questions in Psychotechnic and Dapar Tests

How to solve average questions quickly and accurately, without adding unnecessary numbers

Written by Eli Isaak • Phone: 054-5664932 • Ask me on WhatsApp

About Average Questions

Average questions appear in almost every psychotechnic and Dapar test: student grades, ages, wages, prices, and more. They look simple, but the wording often trips up many examinees, especially when some data are averages and others are sums.

The key to success is to move from the average to the sum. Almost every average question is solved in three steps: calculate the sum (average times quantity), perform the required change on the sum, and finally divide again by the number of elements. Below are 6 core methods for solving the most common types of questions on the test.

The Golden Triangle of Average Questions:

Sum = Average × Quantity
From this, we get the other two forms: Average = Sum / Quantity and Quantity = Sum / Average.
1
Basic Average (Sum Divided by Quantity)
The average of a group of numbers is the value that would be obtained if all numbers were equal to each other. It is calculated as follows: add all the numbers and divide by their count. A number that repeats twice is counted twice.
Example A: Direct Calculation
Five numbers: 6, 8, 10, 14, and 17. What is their average?
  • Sum: 6 + 8 + 10 + 14 + 17 = 55
  • Quantity of numbers: 5
  • Average: 55 / 5 = 11
Answer: 11
Example B: Repeating Value
The ages of five friends are 20, 22, 25, 25, and 33. What is the average age?
  • Sum of ages: 20 + 22 + 25 + 25 + 33 = 125
  • The age 25 appears twice and therefore is counted twice
  • Average: 125 / 5 = 25
Answer: 25 years
2
Finding a Missing Element (Total Sum = Average × Quantity)
When the target average is given, first calculate the total sum it needs to yield (average times quantity), subtract the sum of the known elements from it, and the remainder is the missing element.
Example A: Missing Grade
A student's grades in five tests are 70, 85, 90, 75, and a fifth grade that is unknown. The average of the five grades is 80. What is the fifth grade?
  • Required sum: 80 × 5 = 400
  • Sum of known grades: 70 + 85 + 90 + 75 = 320
  • Missing grade: 400 - 320 = 80
Answer: 80
Example B: Target Grade
The average of a student's first six grades is 82. What grade must they get on the seventh test so that the average of all seven tests is 84?
  • Sum of six grades: 82 × 6 = 492
  • Required sum for seven tests: 84 × 7 = 588
  • Missing grade: 588 - 492 = 96
Answer: 96
3
Change in Average Due to Adding or Removing an Element
In such questions, do not work with averages but with sums: calculate the sum before and after the change, and the difference between them is the element added or removed.
Example A: Added Element
The average of five numbers is 20. When another number is added to them, the average of the six numbers rises to 22. What is the added number?
  • Sum before: 20 × 5 = 100
  • Sum after: 22 × 6 = 132
  • Added number: 132 - 100 = 32
Answer: 32
Example B: Removed Element
The average grade of 30 students in a class is 78. One student left the class, and the average of the 29 remaining students is 79. What was the grade of the student who left?
  • Sum before: 30 × 78 = 2,340
  • Sum after: 29 × 79 = 2,291
  • Leaving student's grade: 2,340 - 2,291 = 49
Answer: 49
4
Weighted Average (Two or More Groups)
When combining groups of different sizes, you must not average the averages. Each average must be counted according to its group size: calculate the sum of each group (average times quantity), add the sums, and divide by the total number of elements.
Example A: Grades
A class has 12 boys with an average grade of 70, and 8 girls with an average grade of 85. What is the average grade of the entire class?
  • Sum of boys: 12 × 70 = 840
  • Sum of girls: 8 × 85 = 680
  • Total sum: 840 + 680 = 1,520, number of students: 12 + 8 = 20
  • Average: 1,520 / 20 = 76
  • Note: The simple average (70 + 85) / 2 = 77.5 is wrong because the groups are unequal in size
Answer: 76
Example B: Prices
You buy 3 kg of apples at 12 NIS per kg and 2 kg of pears at 17 NIS per kg. What is the average price per kg for all the fruit purchased?
  • Cost of apples: 3 × 12 = 36
  • Cost of pears: 2 × 17 = 34
  • Total cost: 36 + 34 = 70 NIS for 5 kg
  • Average price: 70 / 5 = 14
Answer: 14 NIS per kg

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