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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

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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 find the total amount of rainfall for the 28 days, we first add Keith's recorded rainfall:

2.8+5.6+2.3+9.4+0.0+0.5+1.8=22.4 mm2.8 + 5.6 + 2.3 + 9.4 + 0.0 + 0.5 + 1.8 = 22.4 \text{ mm}

Next, we add the total rainfall recorded by Jenny:

( 84.6 \text{ mm} )

Now, the total rainfall over the 28 days is:

22.4+84.6=107 mm22.4 + 84.6 = 107 \text{ mm}

To find the mean amount of rainfall, we divide the total by the number of days:

Mean=107283.82 mm\text{Mean} = \frac{107}{28} \approx 3.82 \text{ mm}

Step 2

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

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Answer

The transposition of the figures affects the mean amount of rainfall. Initially, the figures 9.4 and 0.5 contributed to an incorrect total. The corrected figures, 4.9 and 5.0, will increase the total rainfall since the new numbers are closer to each other and will lead to a more accurate mean.

Thus, the mean will increase slightly because the values of 4.9 and 5.0 are an adjustment from the original figures, where one was significantly higher than it should have been.

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