Three students named Bassey, Okon, and Effiong make measurements (in m) of the length of a table using a metre rule. Complete the table by evaluating, in each case, the mean, the s... Three students named Bassey, Okon, and Effiong make measurements (in m) of the length of a table using a metre rule. Complete the table by evaluating, in each case, the mean, the standard deviation from the mean, and the standard error of the measurements. Read more

Steps to Solve

1. Calculate the Mean ($\bar{L}$)

For each student, the mean length measurement can be calculated using the formula:

$$ \bar{L} = \frac{L_1 + L_2 + L_3 + L_4}{n} $$

where $n$ is the number of measurements (which is 4 for each student).

For each student:

• Bassey: $$ \bar{L} = \frac{1.4717 + 1.4711 + 1.4722 + 1.4715}{4} = \frac{5.8865}{4} = 1.471625 $$

• Okon: $$ \bar{L} = \frac{1.4753 + 1.4759 + 1.4756 + 1.4749}{4} = \frac{5.9017}{4} = 1.475425 $$

• Effiong: $$ \bar{L} = \frac{1.4719 + 1.4723 + 1.4727 + 1.4705}{4} = \frac{5.8874}{4} = 1.47185 $$

2. Calculate the Standard Deviation ($\sigma_{n - 1}$)

The sample standard deviation can be calculated using the formula:

$$ \sigma_{n - 1} = \sqrt{\frac{\sum (L_i - \bar{L})^2}{n - 1}} $$

For each student:

• Bassey: $$ \sigma_{n - 1} = \sqrt{\frac{(1.4717 - 1.471625)^2 + (1.4711 - 1.471625)^2 + (1.4722 - 1.471625)^2 + (1.4715 - 1.471625)^2}{3}} $$

• Okon: $$ \sigma_{n - 1} = \sqrt{\frac{(1.4753 - 1.475425)^2 + (1.4759 - 1.475425)^2 + (1.4756 - 1.475425)^2 + (1.4749 - 1.475425)^2}{3}} $$

• Effiong: $$ \sigma_{n - 1} = \sqrt{\frac{(1.4719 - 1.47185)^2 + (1.4723 - 1.47185)^2 + (1.4727 - 1.47185)^2 + (1.4705 - 1.47185)^2}{3}} $$

3. Calculate the Standard Error ($\alpha$)

The standard error is calculated using:

$$ \alpha = \frac{\sigma_{n - 1}}{\sqrt{n}} $$

For each student, with $n = 4$.

4. Fill in the Table

Complete the table based on the calculated values from steps 1, 2, and 3.