Sam recorded the amount of data (in MB) that she had used on each of the first 15 days in April - NSC Mathematics - Question 1 - 2021 - Paper 2

To calculate the standard deviation, subtract the mean from each data value, square the result, sum these squares, divide by the number of data points, and take the square root.

Calculation:

$\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}} = 17.65 \text{ MB}$

One standard deviation above the mean is:

$\bar{x} + \sigma = 25 + 17.65 = 42.65 \text{ MB}$

Count the days with data greater than 42.65 MB from the dataset:

Total days = 2 days.

The overall mean for 30 days should equal 80% of 25 MB:

$\bar{x}_{overall} = 0.80 \times 25 = 20 \text{ MB}$

Setting an equation for total data:

$375 + x = 30 \times 20$

Solving for x gives:

$x = 600 - 375 = 225\text{ MB}$

Using the least squares method, we find the line:

$y = a + bx$

a = 29.35, b = -0.46\text{, so equation is } y = 29.35 - 0.46x.

Substituting x = 9 into the regression equation:

$y = 29.35 - 0.46(9) = 25.21 °C$

The value of b (-0.46) indicates that for each additional km/h of wind speed, the temperature decreases by approximately 0.46 °C.