Simple calculation from formula (RMSE)

Question

I am using example from here: https://thinkingneuron.com/data-science-interview-questions-for-it-industry/#What-is-RMSE

Root Mean Squared Error:

1. Find out the difference between original and predicted values for each row.
2. Square the differences
3. Sum all squared differences
4. Take the average of the above sum
5. Take the square root of above average

Table:

We see from table that RMSE = 14.2.

Here is what and how I calculated from data presented in table and method described above table:

$(25-20)^{2} + (30-31)^{2} + (29-33)^{2} + (40-38)^{2} = 46$

$\frac{46}{4} = 11.5$

$\sqrt{11.5} = 3.39116$

So in table we have RMSE = 14.2 and from my calculation RMSE = 3.39116. Is there mistake in table or in my calculations?

Answer 1

Good day,

• You sure it is RMSE (Root Mean Square Error)?

• And not MAPE (Mean Absolute pErcentage Error?)

The page seems to be wrong, or your screenshot?

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Actually someone was also confused by this.

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"Hi FARUKH, I find the calculation of RMSE is wrong. Instead of taking the square of APE, it should be the square of the difference between the original and predicted value."

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https://thinkingneuron.com/data-science-interview-questions-for-it-industry/#What-is-RMSE

From the website at

Q. What is RMSE?

Root Mean Squared Error
1. Find out the difference between original and predicted values for each row.
2. Square the differences
3. Sum all squared differences
4. Take the average of the above sum
5. Take the square root of above average

• I also see another problem; with the number of columns. I Think it should be something on those lines:

On the webpage It's 5 columns. In your screenshot It's only 4 columns.

Your screenshot:

Original Predicted
20  25
31  30
33  29
38  40

on the webpage it looks slightly different, and is instead:

Original Predicted

10      12
14      13
18      15
20      23
11      15

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(12-10)²+(14-13)²+(18-15)²+(20-23)²+(11-15)² = 39

39 as in the webpage screenshot

@ SUM: 39

Mean(SUM): 7.8 39/5 = 7.8

RMSE: 2.79 $\sqrt 7,8$ = 2.7928

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webpage screenshot: https://thinkingneuron.com/wp-content/uploads/2020/06/How-to-calculate-RMSE.jpg

This was a interesting question, I'll follow this.

Hope it solves itself.

Regards Will