Page 1 of 1: psm---in a group of 100

lazybonezzz · Credits: 54715 My Scrapbook

kids,
weight of a kid is 15kg
standard error is 1.5 kg
which is true---
195% weigh b/w 12&18kg
295% weigh b/w 13.5 &16.5kg

guest · Credits: 79189 My Scrapbook My Reading List 262569 Books

In practice, one often assumes that data are from an approximately normally distributed population. If that assumption is justified, then about 68% of the values are at within 1 standard deviation away from the mean, about 95% of the values are within two standard deviations and about 99.7% lie within 3 standard deviations. This is known as the "68-95-99.7 rule".

95% of the gaussian distibution lies in between 2 standard deviations of the mean. Here the standard deviation is 1.5 kg and mean is 15 kg. So the answer here is 12 & 18.

lazybonezzz · Credits: 54715 My Scrapbook

well the q says zat the standard error is 1.5kg not the standard deviation
both these r not same .standard error is standard deviation of the means.
park says zat in a normal curve,
95% of the population means lie within 2 standard errors on either side of the sample mean which here is 15 kg(the q mentions a group of 100 kids)
so we get the ans as 12&18
is my logic correct?
wat i cant understand is how every1 equates standard deviation &standard error???

guest · Credits: 79189 My Scrapbook My Reading List 262569 Books

I am so sorry to have missed that fine intricacy. There is definitley a difference between standard error and standard deviation. But the 65, 95, [snip] rule remains the same. Standard error is used for sampling distribution, this is a distribution of averages taken from different samples from same population. e.g. if you take a sample of 100 from these population of kids, its mean may be different from the mean of a sample taken by someone else, and of course the mean of third somebody may be something else. Now these means also have a normal distribution and there the term standard error is used to tell that 95% of the sampling distribtion lies in between two standard errors.

Then what is standard deviation? A standard deviation is the spread of the scores around the average in a single sample. Single sample may be your sample, someone else's sample or third somebody's sample. Same 65, 95, [snip] rule holds there also.

In fact it should have been standard deviation (intead of standard error) in the question because it is single sample.

However the general formula for standard error is standard deviation divided by square root of number of samples. As the number of samples increase the standard error decreases and hence the assumed mean in that sample is more near to original mean of the population.

lazybonezzz · Credits: 54715 My Scrapbook

yes chand this rule holds true
check out park where theyve ginen zat 95% of population means lies on either side of 2 SD of sample mean.soi don think it shud be SD in this q .we can proceed with SE

guest · Credits: 79189 My Scrapbook My Reading List 262569 Books

I very well understand that the same rule holds true for both standard error and standard deviation and I have mentioned it in my post too, but the question given is not that of a sampling distribution, it is just a single sample and that is why it should be standard deviation and not standard error.

Anyway if you feel comfortable with your assessment, I do not need to comment anymore on this.

mickey_p · Credits: 652 My Scrapbook

guest · Credits: 79189 My Scrapbook My Reading List 262569 Books

That was a nice explanation Dr Manish, but if you see the standard deviation becomes 15 in this example if we take 15 as mean and standard error as 1.5 (sample size 100)?? I mean by taking SD 15, 17.5% population should have no weight or weight less than 0. That is why I said it should have been standard deviation and not standard error! I fully agree with you that S.E. can be taken from a single sample but that is not ideal.

mickey_p · Credits: 652 My Scrapbook

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