is the value close enough to 68,95,99.7. Apart from last value others have larger deviation. Or am I doing something wrong.
Hello @Anish_Das123, I think that’s pretty close. We need a perfect bell curve to get exactly those numbers, so any deviation will be explained by why it’s not perfect.
If you examine the data closely, you will find that it spans over many months and roughly two-third of the samples are around August and September.
Now, let’s think about this: now it’s Summer and if we take 10 temperature measurements per second for one minute, that will give us 600 samples of temperature. We believe that the temperature should stay unchanged over that short period but the sample values may still fluctuate due to measurement error. If we plot the distribution of these 600 samples, it is going to be very much like a bell curve. If we had got 60,000 samples in that one minute, it would have looked even closer to a perfect bell curve. My first point here is that, sample size matters.
If we wait until Winter and take another 600 samples in a minute, we should expect a similar result - it looks like a bell curve and would have looked even more like one if we had 60,000 samples. Here comes the beginning of my second point: what if we plot a distribution over the data combining the Summer’s 600 and the Winter’s 600? Is the distribution of these 1,200 samples a bell curve? Obviously not, because we should expect two peaks - one at a higher temperature for the Summer and one at a lower temperature for the Winter. In other words, it is not one bell curve, but two bell curves. Now, our data is a combination of all twelve months, so unless we believed the temperature didn’t change over the year (which is obviously wrong), we shouldn’t expect that to be a bell curve. For the reason why It still looks like a bell curve, I would suggest you to get the counts of each month. My second point is, this data, by its nature, would probably be not normal (not one bell curve), only looks normal (due to the reason you may find by carrying out the counting suggested), so it would not be surprised for having such deviation.
Cheers,
Raymond
Thank you very much.
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No problem, @Anish_Das123!
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