Question

Q.21 :-A national random sample of 20 ACT scores from 2010 is listed below. Calculate the
standard deviation.
29, 26, 13, 23, 23, 25, 17, 22, 17, 19, 12, 26, 30, 30, 18, 14, 12, 26, 17, 18​

Answer 1

Step-by-step explanation:

Answer of this is 20.50

Answer 2

Answer:

The standard deviation of the given sample is 5.941

Standard Deviation:

• Standard deviation gives the measure of variation or dispersion of the values of a given data set.
• It tells how far the data is spread out relative to the mean.
• A low value of standard deviation implies that the values are close to the mean value.
• A high value of standard deviation implies that the values are spread apart from the mean value.
• Standard deviation is given as the square root of the variance.

Step-by-step explanation:

Formula:

σ = $\sqrt{\frac{sum(x-mean)^{2} }{n-1} }$, where n is the number of observations.

Solution:

Substituting the given values, we get

σ = $\sqrt{\frac{670.5499}{20-1} }$

σ = $\sqrt{\frac{670.5499}{19} }$

σ = $\sqrt{35.2921}$

σ = 5.941

Therefore, the standard deviation for the given sample of 20 ACT scores is 5.941

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