Question

Using Excel, give the average and standard deviation of the following set of numbers: {2.777, 1.318, 3.993, 0.310, 1.763, 2.938, 3.431, 3.146, 10.705, 2.526, 1.976, 3.864}. Then plot both the histogram, bucketing the data into 10 evenly spaced bins, and the fitted Gaussian of the latter data in the same spreadsheet, superimposed or overlaid on each other with the same x-axis, on the same printed page.

Answer 1

Average = AVERAGE(A2:A13)

Standard deviation = =STDEV.S(A2:A13)

The results are

Average = 3.23

Std Dev = 2.59

Plotting of Histogram

GIven number of bins = 10

Size of each bin = (Max - Min)/10 = (10.705 - 0.31)/10 = 1.0395

we consider bin size as 1.05

Calss	Frequency
0 - 1.05	1
1.05 - 2.1	3
2.1 - 3.15	4
3.15 - 4.2	4
4.2 - 5.25	0
5.25 - 6.3	0
6.3 - 7.35	0
7.35 - 8.4	0
8.4 - 9.45	0
9.45 - 10.5	0
10.5 - 11.55	1

Histogram 4.5 4 3.5 3 2.5 2 Frequency 1 0.5 0 0 1.05 1.05 2.1 3.15 4.2 5.25 6.3 7.35 8.4 9.45 10.5 2.1 3.15 4,2 5.25 6.3 7,35 8,4 9,45 10.5 11.55 Bin Range st Ln nLn Nu Frequency

Histogram of Data Normal Mean 3.229 6 StDev 2.587 N 12 5 4 1 0 -2 0 8 2 4 6 10 Data co LO LO st Frequency