Question

Q18. Calculate standard deviation for
the following data.
20,22,28,30,35,36,40,45
O A. 8.07
O B. 32
O
C. 10.72
D 12.15​

Answer 1

Step-by-step explanation:

mean=20+22+28+30+35+36+40+45=256

mean=256÷8=32

Answer 2

Answer:

Step-by-step explanation:

Standard Deviation:

• An indicator of how dispersed numbers are is the standard deviation.
• The Greek letter sigma serves as its symbol.
• Its simple formula is the square root of the variance.
• It helps us in comparing data sets with similar means but different ranges.

Variance:

• Variance is the average of the squared differences from the Mean.

Given:

$20,22,28,30,35,36,40,45$

To Find:

We need to calculate the standard deviation.

Solution:

No of observations (n) $=8$

∑$x_{i} = 20+22+28+30+35+36+40+45$

∑$x_{i} = 256$

Mean = ∑$\frac{x_{i}}{n}$

Mean $= 32$

Now,

Finding ∑$(x_{i} -$μ$)^2$,

$20 = (x_{i}-$μ $)^2 = (-12)^2 =144$

Similarly finding ∑$(x_{i} -$μ$)^2$,

$22=100$

$28 =16$

$30=4$

$35=9$

$36=16$

$40=64$

$45=169$

∑$(x_{i} -$μ$)^2$$=522$

Hence, the required standard deviation is:

$=\sqrt{1/n * 522}$

$=\sqrt{1/8 * 522}$

$=\sqrt{65.25}$

$=8.07$

Therefore, the Standard Deviation is $8.07$.

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