Question

given the data 11.4, 11.3, 11.2 and 11.1 cm determine the average and its standard deviation using equation

Answer 1

Answer:

Average  $\bar{x}$ = 11.25 cm

standard deviation = 0.129 cm

Explanation:

The data provided in the question is:

x₁ = 11.4 cm

x₂ = 11.3 cm

x₃ = 11.2 cm

x₄ = 11.1 cm

total number of data points, N = 4

Now, the average is calculated as:

Average $\bar{x}$ = $\frac{sum\ of\ all\ the\ data\ points }{number\ of\ data\ points}$

substituting the values in the above formula we get,

Average  $\bar{x}$ = $\frac{11.4cm+11.3cm+11.2cm+11.1cm }{4}$

Average  $\bar{x}$ = 11.25 cm

Now the standard deviation is calculated as:

standard deviation = $\sqrt\frac{\sum_{i=1}^{4} \left(x_i - \bar x \right )^2}{N-1}$

substituting the values in the above equation we get,

standard deviation = $\sqrt\frac{\left(11.4 - 11.25 \right )^2 + \left(11.3 - 11.25 \right )^2 + \left(11.2 - 11.25 \right )^2 + \left(11.1 - 11.25 \right )^2}{3}$

or

standard deviation = 0.129 cm