Give the picture , Mean: 3.487783 and Standard deviation: 1.141371 a. How does t

Question

Give the picture , Mean: 3.487783 and Standard deviation: 1.141371

a. How does this distribution compare to the standard normal distribution in terms of shape?

b. Using the histogram, approximately how much of the eruption data falls within 1 standard deviation of the mean? How does this compare to the Empirical Rule that applies to nearly-normal data? This percentage is something you can “eyeball” estimate from Mean , Standard deviation and the bin frequencies.

Explanation / Answer

a.) standard normal distribution is bell shaped but as we see in this histogram, it is not a bell shaped figure. So this distribution is not normal

b.) for the data to fall within 1 standard deviation of mean, means to fall in the range

Mean-standard deviation and Mean+standard deviation

i.e 3.487783-1.141371 and 3.487783+1.141371

2.35 and 4.63 approx

So the data should lie in this range to fall within 1 standard deviation of mean

Now we see from the given histogram

Total frequency= 16+40+19+15+4+4+3+1+5+9+7+22+25+28+40+24+12+4

=252

So the total frequency is approximately 252, from the histogram given.

And the frequency of data lying in the range 2.35 to 4.63 =4+4+3+1+5+9+7+22+25+28+40

=148

So data falling within 1 standard deviation of mean is 148.

And this is (148*100)÷252 = 58.7% of the entire data set.

According to emperical rule, 68% of the data falls within 1 standard deviation of mean in a nearly normally distributed data.

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