Question

Interpreting Standard Deviation Standard deviation is a measure of the typical amount an entry deviates from the mean. Example 10 Match the standard deviations with the plot: 8.59 7.29 1.07 4.08 1.60 C1 C2 C3 C5 12 Data 9 15 18 21

Answer 1

The more the entries are spread out, the greater the standard deviation.

In C1,C2,C3&C5 have symmetrical distribution about 12 but in C4 distribution asymmetrical.

Standard deviation of C4 can be calculated as:

$\bar{x}=$(3*1+4*1+11*5+12*6+13*4+20*1+21*1)/19=11.94

$\sigma _{c4}=\sqrt{\frac{\sum (x-\bar{x})^{2}}{n-1}}= \sqrt{\frac{ 1\times (3-11.94)^{2}+1\times (4-11.94)^{2}+5\times (11-11.94)^{2}+6\times (12-11.94)^{2}+4\times (13-11.94)^{2}+1\times (20-11.94)^{2}+1\times (21-11.94)^{2}}{19-1}}$

=$\sqrt{\frac{ (3-11.94)^{2}+(4-11.94)^{2}+5\times (11-11.94)^{2}+6\times (12-11.94)^{2}+4\times (13-11.94)^{2}+(20-11.94)^{2}+(21-11.94)^{2}}{18}}$

$=\sqrt{\frac{298.94}{18}}=\sqrt{16.60}\approx 4.08$

similarly, it'll be followed for others.

Thus, the matching will be as follows:

8.59	7.29	1.07	4.08	1.60
C3	C5	C1	C4	C2

I hope this would help you, if you still have any doubt please let me know.