Question

Calculating the standard deviation (σ) for a list of n data values: 1. Calculate the average value. 2. Subtract the average value from each individual data value and enter the results in a column to the right of the data values. 3. Square each of the results obtained in step 2, and enter these in a new column to the right. 4. Sum the squares obtained in step 3. 5. Divide the result from step 4 by (n - 1) (the total number of measurements minus 1). 6. Take the square root of the result from step 5. This is the standard deviation. Expressed as an equation, the standard deviation of n measurements of data value x is: σ = ( Σ (x - xavg)2 / (n - 1) )1/2 Using the 6 steps above (or the spreadsheet function), calculate the standard deviation for the six values on page 16 and enter your answer below. Enter your result with only one sig fig, and remember to use a zero before the decimal point for values less than 1, for example 0.05 or 0.01.

Answer 1

Explanation:

The missing list of the data values for the question are as follows:

1 1.03

2 1.01

3 0.96

4 0.96

5 0.99

6 1

7 1.01

8 0.98

9 1.02

10 1.03

11 1

12 0.99

13 1

14 0.97

15 1.01

`x_i`
`(x_i - \bar x)`
`(x_i - \bar x)^2`

1 1.03 0.03 0.0009

2 1.01 0.01 0.0001

3 0.96 -0.4 0.0016

4 0.96 -0.4 0.0016

5 0.99 -0.1 0.0001

6 1 0.0 0.0

7 1.01 0.1 0.0001

8 0.98 -0.2 0.0004

9 1.02 0.2 0.0004

10 1.03 0.3 0.0009

11 1 0.0 0.0

12 0.99 -0.1 0.0001

13 1 0.0 0.0

14 0.97 -0.03 0.0009

15 1.01 0.1 0.0001

The average value for x is calculated as:

`\bar x = (14.96)/(15)`

`\bar x = 0.997 \\ \\ \bar x \approx 1.00`

`\sum (x-x_i)^2 = 0.0072`

`(\sum (x-x_i)^2 )/(n-1)= (0.0072)/(15-1) \\ \\ = (0.0072)/(14) \\ \\ = 0.00051`

`\sigma = \sqrt{(\sum (x-x_i)^2 )/(n-1)} = √(0.00051) \\ \\ \sigma =0.0226 \\ \mathbf { \\ \sigma =0.02 \ to \ one \ significant \ figure}`