Average Questions for UP POLICE CONSTABLE

What is Average?

Average (or arithmetic mean) is the sum of all values divided by the count of values. Think of it as 'fair share' — if you pool all money and distribute equally, everyone gets the average. In UP Police exams, average questions often disguise themselves as word problems about ages, salaries, marks, or distances. The core formula never changes, but the context does.

• Average = Total Sum / Number of Items
• Rearranged: Total Sum = Average × Number of Items
• Average is always between the smallest and largest value in the set
• If all values are equal, average equals that value
• Average can be a decimal or fraction, not always a whole number

Average in Word Problems

UP Police loves disguising average in real-world contexts. A question might ask about average age of a group, average salary, average distance traveled, or average marks. The trick is to identify that it's an average problem, extract the numbers, and apply the formula. Read carefully for keywords like 'on average', 'mean', 'equally', or 'fair share'.

• Identify the keyword: 'average', 'mean', 'on average', 'equally distributed'
• Extract: what are we averaging (ages, salaries, marks)?
• Count: how many items are in the group?
• Calculate: use Total = Average × Count or vice versa
• Check: does your answer make sense (between min and max)?

Weighted Average

Sometimes items in a group have different importance or frequency. For example, if 3 students scored 80 and 2 students scored 90, the average is not (80 + 90) / 2 = 85. Instead, you weight by frequency: (80×3 + 90×2) / (3+2) = (240 + 180) / 5 = 84. UP Police occasionally tests this in moderate-difficulty questions. The key is to multiply each value by its weight (frequency or quantity) before summing.

• Weighted Average = (Sum of (Value × Weight)) / (Sum of Weights)
• Weight can be frequency, quantity, or importance
• Always multiply value by its weight before adding
• Divide by total weight, not by number of distinct values
• Common in salary, age, or marks problems with groups

Average Increase/Decrease

A common UP Police pattern: 'Average was X, then a new person/item joined, average became Y. Find the new person's value.' Or: 'Average was X, one person left, average became Y. Find that person's value.' These require you to calculate totals before and after, then find the difference.

• Calculate old total: old average × old count
• Calculate new total: new average × new count
• Difference = new total - old total = value of person who joined/left
• If average increases, the new person has above-average value
• If average decreases, the new person has below-average value

• Confusing average with total: If average is 50 and count is 10, total is 500, NOT 50. Many aspirants forget to multiply.
• Forgetting to count correctly: In weighted average, the denominator is total weight, not number of groups. If 3 people have age 25 and 2 people have age 30, denominator is 5, not 2.
• Assuming average is always a whole number: Average can be 33.75 or 42.5. Don't round unless the question asks.
• Misreading 'per' or 'each': 'Average salary per person' means total salary / number of people. Don't mix up the direction.
• Ignoring the range check: If smallest value is 10 and largest is 50, average must be between 10 and 50. If your answer is 60, you made an error.

• AVERAGE = TOTAL / COUNT. Rearranged: TOTAL = AVERAGE × COUNT. (This is the golden rule — memorize both directions.)
• Think 'Fair Share': Average is what everyone gets if you pool and divide equally. Helps you sense-check answers.
• Weighted Average = (Value × Weight) summed, then divided by total weight. Mnemonic: VW over W (Value-Weight over total Weight).
• Increase/Decrease: New Total - Old Total = New Person's Value. (Subtract the totals, not the averages.)

• UP Police typically asks 2-3 average questions per paper, mostly easy to moderate. Expect at least one word problem disguised as a real-world scenario (ages, salaries, distances).
• Time management: Average questions should take 1-2 minutes max. If you're stuck, move on and come back. These are not meant to be time-sinks.
• Watch for multi-step problems: A question might ask average, then ask 'if one person leaves, what is new average?' Practice these chains.
• Weighted average is less common but appears in 1 in 5 papers. If you see 'groups' or 'frequencies', think weighted average immediately.
• Calculators are NOT allowed in UP Police. Practice mental math for multiplication and division. For example, 26 × 5 should be instant (130).