Keith records the amount of rainfall, in mm, at his school, each day for a week. The results are given below. 2.8 5.6 2.3 9.4 0.0 0.5 1.8 Jenny then records the amount of rainfall, x mm, at the school each day for the following 21 days. The results for the 21 days are summarised below. ∑x = 84.6 (a) Calculate the mean amount of rainfall during the whole 28 days. Keith realises that he has transposed two of his figures. The number 9.4 should have been 4.9 and the number 0.5 should have been 5.0. Keith corrects these figures. (b) State, giving your reason, the effect this will have on the mean.

A-Level Edexcel Maths Statistics Working with Data: Keith records the amount of rain

Keith records the amount of rainfall, in mm, at his school, each day for a week - Edexcel - A-Level Maths Statistics - Question 2 - 2011 - Paper 1

Question 2

Keith records the amount of rainfall, in mm, at his school, each day for a week. The results are given below. 2.8 5.6 2.3 9.4 0.0 0.5 1.8 Jenny then records ... show full transcript

Worked Solution & Example Answer:Keith records the amount of rainfall, in mm, at his school, each day for a week - Edexcel - A-Level Maths Statistics - Question 2 - 2011 - Paper 1

Step 1

Calculate the mean amount of rainfall during the whole 28 days.

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Answer

To calculate the mean rainfall over the 28 days, we first sum the rainfall amounts observed over the week and the total rainfall for the following 21 days.

The total rainfall for the week is:

$ext{Total for week} = 2.8 + 5.6 + 2.3 + 9.4 + 0.0 + 0.5 + 1.8 = 22.4 ext{ mm}$

Adding this to the total for the subsequent 21 days:

$ext{Total for 28 days} = 22.4 + 84.6 = 107 ext{ mm}$

Now, to find the mean:

$ext{Mean} = \frac{ ext{Total rainfall}}{ ext{Number of days}} = \frac{107}{28} \approx 3.8214 ext{ mm}$

Step 2

State, giving your reason, the effect this will have on the mean.

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Answer

When Keith corrects his figures from 9.4 to 4.9 and 0.5 to 5.0, the total rainfall will decrease by 4.9 - 9.4 + 5.0 - 0.5 = -1.9 mm.

This means that the corrected total rainfall will now be:

$ext{New Total for 28 days} = 107 - 1.9 = 105.1 ext{ mm}$

Consequently, the new mean will be:

$ext{New mean} = \frac{105.1}{28} \approx 3.75 ext{ mm}$

Thus, the mean will decrease as a result of these corrections.

Keith records the amount of rainfall, in mm, at his school, each day for a week - Edexcel - A-Level Maths Statistics - Question 2 - 2011 - Paper 1

Worked Solution & Example Answer:Keith records the amount of rainfall, in mm, at his school, each day for a week - Edexcel - A-Level Maths Statistics - Question 2 - 2011 - Paper 1

Calculate the mean amount of rainfall during the whole 28 days.

State, giving your reason, the effect this will have on the mean.

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