I've attached the photo below with the question. I am not able to attached the excel file with the data but these are the answers I got when I calculated the Standard deviation and Interquartile Range. I am struggling to understand what I am expected to do with the data and what explanation I need to give 

 

Standard deviation for 100 = 0.9888544404

                                       1000 = 0.99179207

                                      10000 = 1.00031618

 

Interquartile Range for 100 = 1.27660118

                                       1000 = 1.33530429

                                      10000 = 1.3492011

If data follows a normal distribution in the population (we cover this later), then the interquartile range and standard deviation are related. The dataset Interquartile Range verses Standard Deviation.xIsx contains three sheets: the first has 100 samples, the second has 1000 and the third has 10000. For each of them, calculate the interquartile range and standard deviation, and see whether the following formula holds approximately: Interquartile Range Standard Deviation = 1.3489795 Explain your reasoning. For example, does this formula become closer to becoming true as the sample size increases?

From the computed standard deviation and interquartile range of samples 100, 1000 and 10000, it was observed that as the sample size increase and becomes bigger and bigger, the formula that describes the relationship between the standard deviation and interquartile range is closer of becoming true. This is because as the formula is being applied to the samples, the left and right side of the equation are getting closer and closer to becoming equal. Thus we can say that the data follows a normal distribution.

Please see explanation and calculations below.

Step-by-step explanation

Hello good day. Okay let me explain the answer to your question.

The problem asks you to determine whether the data you calculated follows a normal distribution. If the data follows a normal distribution, then the standard deviation and interquartile range are related and this relationship is expressed in the given formula below.

So what we will actually do is that from the standard deviation and interquartile range you have calculated, we will see if the formula stands that both values are becoming equal as the sample size increase so that later on we will conclude that the data follows a normal distribution.

So for a sample of 100, the standard deviation is 0.9888544404 and the interquartile range is 1.27660118. Applying the formula we have:

 0.9888544404=1.34897951.27660118?

Then we simplify the right side we have 0.9888544404=0.9463458711

So for this number of sample, we will notice that the left and right are not equal but close.

For a sample of 1000, the standard deviation is 0.99179207 and interquartile range is 1.33530429. Substitute in the formula we have:

0.99179207=1.34897951.33530429?

Simplify the right side we have 0.99179207=0.9898625517

Now we notice that as we increased the sample to sample to 1000, the left and the right side becomes even very close.

Finally for a sample of 10000, the standard deviation is 1.00031618 and the interquartile range is 1.3492011. Substitute in the formula we have:

1.00031618=1.34897951.3492011?

Simplify the right side we have 1.00031618=1.000164272

Now for this one, we see that the left and the right side now is nearly equal.

So with these, we see that as we increase our sample size, the formula, which describes the relationship of standard deviation and interquartile range are closer of becoming true. So with that, we can generalize that the formula is true with the number of sample size increases and thus the data we have follows a normal distribution.