Stav is studying the large data set for September 2015 He codes the variable Daily Mean Pressure, x, using the formula y = x - 1010 The data for all 30 days from Hurn are summarised by ∑y = 214 ∑x² = 5912 (a) State the units of the variable x (b) Find the mean Daily Mean Pressure for these 30 days - Edexcel - A-Level Maths Statistics - Question 3 - 2021 - Paper 1

To find the mean Daily Mean Pressure, we use the formula:

ar{x} = rac{ ext{Sum of } x}{n}

Substituting the given values:

ar{x} = rac{214}{30} + 1010 = 7.1333 + 1010 \\ = 1017.1333 ext{ hPa}

Thus, the mean Daily Mean Pressure is approximately 1017 hPa.

The standard deviation can be calculated using the formula:

ext{Standard Deviation} = rac{ ext{Sum of } x^2 - rac{( ext{Sum of } x)^2}{n}}{n}

To calculate:

ext{Standard Deviation} = rac{5912 - rac{(214)^2}{30}}{30} = rac{5912 - rac{45796}{30}}{30}

Calculating the values:

ext{Standard Deviation} = rac{5912 - 1525.3333}{30} = rac{4386.6667}{30} \\ = 146.2222 ext{ hPa}

Thus, the standard deviation of Daily Mean Pressure is approximately 146.22 hPa.

According to the information, high pressure circulates winds in a clockwise direction. Hence, based on the locations relative to each other:

• The location of higher pressure is Leuchars, as it is to the north of the other two locations, so it should be placed clockwise.
• Therefore, the Cardinal Wind Directions are as follows:
  • Heathrow (W)
  • Hurn (N)
  • Leuchars (E)

This placement is justified as it follows the direction of decreasing pressure.