Question

find the standard deviation of 4,8, 10, 12 and 16​

Answer 1

Given:

4, 8, 10, 12 and 16​

To find:

The standard deviation

Solution:

The required value is 4.

The given terms are 4, 8, 10, 12, 16.

The number of terms=5

We will obtain the mean value and then calculate the square of the difference between each term and the mean.

The mean=Sum of terms/Number of terms

Mean=(4+8+10+12+16)/5

=50/5

=10

Now, the difference between terms and the mean is as follows-

4-10= -6

8-10= -2

10-10=0

12-10=2

16-10=6

Squaring the obtained values and adding them,

= $(-6)^{2} +(-2)^{2} +0^{2} +2^{2} +6^{2}$

=36+4+4+36

=80

The standard deviation of the terms=Square root of the sum of squares of values divided by the number of terms

=$\sqrt{80/5}$

=$\sqrt{16}$

=4

Therefore, the required value is 4.

Answer 2

The standard deviation will be 4.

Step-by-step explanation:

Given numbers 4, 8, 10, 12, 16

=> Formula for standard deviation is given below ,

$\sqrt{\frac{x_{1} ^{2} +x_{2} ^{2} +x_{3} ^{2}+ upto x_{n} ^{2} }{n} - (\frac{x_{1} +{x_{2} }+{x_{3} }upto{x_{n} }}{n} )^{2} }$

Substituting the values ,

$\sqrt{\frac{4 ^{2}+8 ^{2}+10 ^{2}+12^{2}+16^{2} }{5} - (\frac{4 +8+ 10+ 12+16}{5})^{2}$

$\sqrt{\frac{580 }{5} - (\frac{50}{5})^{2}$

$\sqrt{116-100}$

$\sqrt{16}$

= 4

Therefore the standard deviation of 4, 8, 10, 12, 16 is 4