Question

What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125?

Answer 1

Answer:

18.24 (approx)

Step-by-step explanation:

The mean is

( 75 + 83 + 96 + 100 + 121 + 125 ) / 6 = 600 / 6 = 100

The deviations from the mean are:

75 - 100 = -25          83 - 100 = -17          96 - 100 = -4

100 - 100 = 0          121 - 100 = 21          125 - 100 = 25

The variance is the mean of the squares of these deviations:

( 25² + 17² + 4² + 0² + 21² + 25² ) / 6 = 998 / 3 ≈ 332.6667

The standard deviation is the square root of the variance:

√332.6667 ≈ 18.24

Answer 2

The standard deviation is "332.6667".

Step-by-step explanation:

To find, the standard deviation = ?

We know that,

Mean $=\dfrac{Sum of the observations}{Total number of observations}$

$=\dfrac{75+83+96+100+121+12 }{6}$

$=\dfrac{600}{6}=100$

The deviations from the mean are:

75 - 100 = -25, 83 - 100 = -17, 96 - 100 = - 4, 100 - 100 = 0, 121 - 100 = 21    and 125 - 100 = 25

∴ The variance is the mean of the squares of these deviations:

$=\dfrac{25^2+17^2+4^2+ 0^2+21^2+25^2}{6}$

$=\dfrac{625+289+16+0+441+625}{6}$

$=\dfrac{1996}{6}$

$=\dfrac{998}{3}$

≈ 332.6667

Hence, the standard deviation is 332.6667.