Question

the number Of books read by 8 students during a month are 2,5,8,11,14,6,12 and 10.calculate the standard deviation of the data.​

Answer 1

Answer:

For calculating the standard deviation of the above-given data, let us first calculate certain information from the calculated data of tabular figure attached below:

N = 8  

Mean, µ = ∑X / N = 68 / 8 = 8.5

Sum of the square of the deviations, ∑(X-µ)² = 112

Now, the standard deviation of the data is given as,

σ = √ [{∑(X-µ)²} / N]

⇒ σ = √ [112/8]

⇒ σ = √14

⇒ σ = 3.741

Thus, the standard deviation of the given data for 8 students is 3.714.  

Answer 2

Answer:

The standard deviation of the number of books read by 8 students is 3.741

Step-by-step explanation:

Let us begin by understanding the steps in calculating Standard Deviation of a given data.

1. We find the mean (average) of the given data.
2. For each given number, we subtract the mean from the given number and square the difference.
3. We calculate the mean (average) of the squared differences.
4. Square root of the mean calculated in step 3 gives us the standard deviation of the data.

Step 1:

    Mean of the given data = $\frac{2+5+8+11+14+6+12+10}{8} = \frac{68}{8} = 8.5$

Step 2:

    Subtracting each number from the mean and squaring the difference, we have:

• $(2-8.5)^{2} = (-6.5)^{2} = 42.25$
• $(5-8.5)^{2} = (-3.5)^{2} = 12.25$
• $(8-8.5)^{2} = (-0.5)^{2} = 0.25$
• $(11-8.5)^{2} = (2.5)^{2} = 6.25$
• $(14-8.5)^{2} = (5.5)^{2} = 30.25$
• $(6-8.5)^{2} = (-2.5)^{2} = 6.25$
• $(12-8.5)^{2} = (3.5)^{2} = 12.25$
• $(10-8.5)^{2} = (1.5)^{2} = 2.25$

Step 3:

   Mean of the squared differences =

$\frac{42.25+12.25+0.25+6.25+30.25+6.25+12.25+2.25}{8} = \frac{112}{8}$

=14

Step 4:

The Standard deviation of the given data is:

$\sqrt{14}$ = 3.741

Thus, the standard deviation of the number of books read by 8 students is: 3.741