# Calculating Correct Arithmetic Mean

One of the easiest and scoring topics under arithmetic mean is calculating the correct arithmetic mean. No need to learn complicated formulas, just remember the individual series direct method formula and apply some logic.

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## Calculation of ‘Corrected Arithmetic Mean’

Let’s start directly with a question.

**The mean value of the weekly income of 40 families is Rs.265. But in the calculation, the income of one family was read as 150 instead of 115. Find the “Corrected” mean.**

**Solution.**

**Step 1 – Find Summation X**

The trick is simple, read the question. Step by step, start writing down whatever is given.

N = 40

Mean = 265

So, far I extracted information from the first line only. Since I have N and mean. Now, I will apply the direct formula of the arithmetic mean;

I will find summation X.

265 = Summation X/ 40

Summation X = 10600

**Step 2 – Whatever is wrong, it should be subtracted and whatever is correct, it should be added. In Summation X from step 1.**

Now, Continue further with the question;

Wrong value = 150 (It should be subtracted)

Correct value = 115 (It should be added)

**New Summation X = 10600 – 150 + 115 = 10565**

**Step 3 – Now apply the formula and find the correct arithmetic mean with the updated information.**

**Correct Arithmetic Mean = 10565/ 40 = 264.125**

Let’s try one more question, involving 2 incorrect observations.

**2. The mean of 5 observations is 7. Later on, it was found that two observations 4 and 8 were wrongly taken instead of 5 and 9. Find the corrected mean. **

Solution.

We will follow the same 3 steps.

**Step 1 – Find Summation X**

The trick is simple, read the question. Step by step, start writing down whatever is given.

N =. 5

Mean = 7

Apply the above formula to find summation X.

7 = Summation X/ 5

Summation X = 35

**Step 2 – Whatever is wrong, it should be subtracted, and whatever is correct, should be added. In Summation X from step 1.**

Wrong X = 4 and 8

Correct X = 5 and 9

**New Summation X = 35 – 4 – 8 + 5 + 9 = 37**

**Step 3 – Now apply the formula and find the correct arithmetic mean with the updated information.**

Correct Mean = New Summation X/ N

**Correct Arithmetic Mean = 37/5 = 7.4**

You can watch my video on the calculation of correct arithmetic mean, below:

Now, Try some questions on your own.

## Test Yourself

- Mean marks obtained by 100 students are estimated to be 40. Later on, it is found that one value was read as 83 instead of 53. Find out the “corrected mean”. (Answer – 39.70)
- The mean of 100 observations is found to be 40. If at the time of computation two items are wrongly taken as 30 and 27 instead of 2 and 72, find the correct mean. (Answer – 40.18)

I hope it was helpful, you can refer more posts related to the statistics.

- Individual Series Arithmetic Mean
- Discrete Series Arithmetic Mean
- Continuous Series Arithmetic Mean
- Inclusive and Exclusive Series – Arithmetic mean
- Introduction to the statistics.
- Functions and importance of statistics.

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