Standard deviation of 10, 12, 9, 8, 21 is (correct to two decimals):

The correct option is 4.69.

Step 1: Understand the definition of Standard Deviation
Standard deviation measures the amount of variation or dispersion of a set of values from its mean. The formula for the population standard deviation ($\sigma$) is given by:

$\sigma =\sqrt{\frac{\sum {(x_i-\overline{x})}^2}{N}}$

where:
• $x_i$ represents each individual data value,
• $\overline{x}$ represents the mean of the data values,
• $N$ is the total number of values.

Step 2: Find the mean ($\overline{x}$)
The given data set is: 10, 12, 9, 8, 21.
Total number of values ($N$) = 5.
Sum of all values = 10 + 12 + 9 + 8 + 21 = 60.

$\overline{x}=\frac{60}{5}=12$

Step 3: Calculate the squared deviations from the mean ${(x_i-\overline{x})}^2$
For each number, subtract the mean (12) and square the result:
• For 10: ${(10-12)}^2={\left(-2\right)}^2=4$
• For 12: ${(12-12)}^2={\left(0\right)}^2=0$
• For 9: ${(9-12)}^2={\left(-3\right)}^2=9$
• For 8: ${(8-12)}^2={\left(-4\right)}^2=16$
• For 21: ${(21-12)}^2={\left(9\right)}^2=81$

Step 4: Sum the squared deviations
Sum = 4 + 0 + 9 + 16 + 81 = 110.

Step 5: Calculate Variance and Standard Deviation
Variance (${\sigma }^2$):

${\sigma }^2=\frac{110}{5}=22$

Standard Deviation ($\sigma$):

$\sigma =\sqrt{22}\approx 4.6904$

Rounding to two decimal places gives 4.69.