Question

Select at random by yourself, without consulting with anybody else, FIVE intervals such that each of them is contained in the interval of [0,20] and has a length between 5 and 10. (Note that selecting five identical sets of the five ranges by two different students is practically zero.)(ii)For each i = 1, 2, 3, 4 and 5, in column i of an Excel worksheet, generate 30,000 uniform random numbers according to interval i selected in part (i).(iii)For each of the 30,000 rows, calculate the SUM of the 5 random numbers, not the average, and store the 30,000 sums in Column 6.(iv)Create 1000 bins in Column 8.(v)Plot the histogram of the sums. (You may need a better set of bins to allow a proper study of the shape.)(vi)Also plot the histogram of any of Columns 1 through 5. (You may need a better set of bins to allow a proper study of the shape.)(vii)Comment on the two different shapes and state the phenomenon.(viii) Now, for each of the 30,000 rows, calculate the AVERAGE of the 5 random numbers and store the 30,000 sums in Column 7. (ix)Plot the histogram of the averages. (x)Comment on the differences between the shape of the histogram of the sums and that of the averages.

Answer #1

Step1:

randomize the data using randbetween command in excel:For example

Col1:randbetween(2,8) drag it for 30000 rows. repeat the same procedure to create another 4 columns with different interval.

Step2:

Store the sum in col6=sum(col1:col5)

Step3:

give the random bins

Step4:

Store the avg in col7 = average(col1:col5)

Histogram are as follows:

Histogram if sum

Histogram of average:

Histogram of single column:

#Shape of both avg and sum histogram is same but mean changes.

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