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Parents Pricing Home A-Level AQA Maths Mechanics Quantities, Units & Modelling The table below shows the temperature on Mount Everest on the first day of each month
The table below shows the temperature on Mount Everest on the first day of each month - AQA - A-Level Maths Mechanics - Question 11 - 2020 - Paper 3 Question 11
View full question The table below shows the temperature on Mount Everest on the first day of each month.
Month
Temperature (°C)
Jan -17 Feb -16 Mar -14 Apr -9 May -2 Jun ... show full transcript
View marking scheme Worked Solution & Example Answer:The table below shows the temperature on Mount Everest on the first day of each month - AQA - A-Level Maths Mechanics - Question 11 - 2020 - Paper 3
Calculate the Mean Temperature Only available for registered users.
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To find the mean temperature, sum all the temperatures and then divide by the number of months (12):
ext{Mean} = rac{-17 + (-16) + (-14) + (-9) + (-2) + 2 + 6 + 5 + (-3) + (-4) + (-11) + (-18)}{12}
Calculating this gives:
ext{Mean} = rac{-81}{12} = -6.75 .
Calculate Variance Only available for registered users.
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The variance is calculated as the average of the squared differences from the Mean:
ext{Variance} = rac{1}{n} imes igg( ext{sum}(( ext{temperature} - ext{Mean})^2) igg)
Calculating each term:
( − 17 − ( − 6.75 ) ) 2 = ( − 10.25 ) 2 = 105.0625 (-17 - (-6.75))^2 = (-10.25)^2 = 105.0625 ( − 17 − ( − 6.75 ) ) 2 = ( − 10.25 ) 2 = 105.0625 ( − 16 − ( − 6.75 ) ) 2 = ( − 9.25 ) 2 = 85.5625 (-16 - (-6.75))^2 = (-9.25)^2 = 85.5625 ( − 16 − ( − 6.75 ) ) 2 = ( − 9.25 ) 2 = 85.5625 ( − 14 − ( − 6.75 ) ) 2 = ( − 7.25 ) 2 = 52.5625 (-14 - (-6.75))^2 = (-7.25)^2 = 52.5625 ( − 14 − ( − 6.75 ) ) 2 = ( − 7.25 ) 2 = 52.5625 ( − 9 − ( − 6.75 ) ) 2 = ( − 2.25 ) 2 = 5.0625 (-9 - (-6.75))^2 = (-2.25)^2 = 5.0625 ( − 9 − ( − 6.75 ) ) 2 = ( − 2.25 ) 2 = 5.0625 ( − 2 − ( − 6.75 ) ) 2 = ( 4.75 ) 2 = 22.5625 (-2 - (-6.75))^2 = (4.75)^2 = 22.5625 ( − 2 − ( − 6.75 ) ) 2 = ( 4.75 ) 2 = 22.5625 ( 2 − ( − 6.75 ) ) 2 = ( 8.75 ) 2 = 76.5625 (2 - (-6.75))^2 = (8.75)^2 = 76.5625 ( 2 − ( − 6.75 ) ) 2 = ( 8.75 ) 2 = 76.5625 ( 6 − ( − 6.75 ) ) 2 = ( 12.75 ) 2 = 162.5625 (6 - (-6.75))^2 = (12.75)^2 = 162.5625 ( 6 − ( − 6.75 ) ) 2 = ( 12.75 ) 2 = 162.5625 ( 5 − ( − 6.75 ) ) 2 = ( 11.75 ) 2 = 138.0625 (5 - (-6.75))^2 = (11.75)^2 = 138.0625 ( 5 − ( − 6.75 ) ) 2 = ( 11.75 ) 2 = 138.0625 ( − 3 − ( − 6.75 ) ) 2 = ( 3.75 ) 2 = 14.0625 (-3 - (-6.75))^2 = (3.75)^2 = 14.0625 ( − 3 − ( − 6.75 ) ) 2 = ( 3.75 ) 2 = 14.0625 ( − 4 − ( − 6.75 ) ) 2 = ( 2.75 ) 2 = 7.5625 (-4 - (-6.75))^2 = (2.75)^2 = 7.5625 ( − 4 − ( − 6.75 ) ) 2 = ( 2.75 ) 2 = 7.5625 ( − 11 − ( − 6.75 ) ) 2 = ( − 4.25 ) 2 = 18.0625 (-11 - (-6.75))^2 = (-4.25)^2 = 18.0625 ( − 11 − ( − 6.75 ) ) 2 = ( − 4.25 ) 2 = 18.0625 ( − 18 − ( − 6.75 ) ) 2 = ( − 11.25 ) 2 = 126.5625 (-18 - (-6.75))^2 = (-11.25)^2 = 126.5625 ( − 18 − ( − 6.75 ) ) 2 = ( − 11.25 ) 2 = 126.5625
Now summing all these squared differences:
105.0625 + 85.5625 + 52.5625 + 5.0625 + 22.5625 + 76.5625 + 162.5625 + 138.0625 + 14.0625 + 7.5625 + 18.0625 + 126.5625 = 750.875 105.0625 + 85.5625 + 52.5625 + 5.0625 + 22.5625 + 76.5625 + 162.5625 + 138.0625 + 14.0625 + 7.5625 + 18.0625 + 126.5625 = 750.875 105.0625 + 85.5625 + 52.5625 + 5.0625 + 22.5625 + 76.5625 + 162.5625 + 138.0625 + 14.0625 + 7.5625 + 18.0625 + 126.5625 = 750.875
Then, dividing by 12 to get the variance:
eq 62.57291667 $$
Calculate Standard Deviation Only available for registered users.
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The standard deviation is the square root of the variance:
e x t S t a n d a r d D e v i a t i o n = e x t s q r t ( 62.57291667 ) = 7.91 ext{Standard Deviation} = ext{sqrt}(62.57291667) \\ = 7.91 e x t St an d a r d De v ia t i o n = e x t s q r t ( 62.57291667 ) = 7.91
Select the Correct Answer Only available for registered users.
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Comparing the calculated standard deviation with the provided options, the correct answer is:
8.24
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