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

Average
`\bar{x}` = 11.25 cm

standard deviation = 0.129 cm

Step-by-step 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}` =
`(sum\ of\ all\ the\ data\ points )/(number\ of\ data\ points)`

substituting the values in the above formula we get,

Average
`\bar{x}` =
`(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(\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(\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