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The partially completed box plot in Figure 1 shows the distribution of daily mean air temperatures using the data from the large data set for Beijing in 2015 - Edexcel - A-Level Maths Statistics - Question 2 - 2019 - Paper 1

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The partially completed box plot in Figure 1 shows the distribution of daily mean air temperatures using the data from the large data set for Beijing in 2015. An ou... show full transcript

Worked Solution & Example Answer:The partially completed box plot in Figure 1 shows the distribution of daily mean air temperatures using the data from the large data set for Beijing in 2015 - Edexcel - A-Level Maths Statistics - Question 2 - 2019 - Paper 1

Step 1

Complete the box plot in Figure 1 showing clearly any outliers.

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Answer

To complete the box plot, the following steps should be taken:

  • First, determine the interquartile range (IQR): IQR = Q3 - Q1.
  • Using the provided values for the three lowest temperatures (7.6°C, 8.1°C, and 9.1°C) and the maximum temperature (32.5°C), calculate the quartiles if not given explicitly.
  • Any values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR should be marked as outliers. In this case, the two outliers are 7.6°C and 32.5°C.
  • These values will be plotted on the box plot along with the rest of the data.

Step 2

Using your knowledge of the large data set, suggest from which month the two outliers are likely to have come.

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Answer

The two outliers are likely to have come from October, as that is typically the month with the coldest temperatures between May and October in Beijing.

Step 3

Show that, to 3 significant figures, the standard deviation is 5.19°C.

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Answer

To calculate the standard deviation:

  1. Use the formula: S = rac{ ext{sqrt}{{ rac{Σx^2}{n}}} - rac{(Σx)^2}{n^2}}
  2. Compute the variance: S^2 = rac{4952.906}{184} - rac{(4153.6)^2}{184^2}
  3. Calculate the standard deviation, rounding to three significant figures yields 5.19°C.

Step 4

Using Simon's model, calculate the 10th to 90th interpercentile range.

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Answer

To calculate the 10th to 90th interpercentile range using Simon's model:

  1. Identify the Z-scores for the 10th and 90th percentiles. These are approximately -1.2816 and 1.2816, respectively.
  2. Use the formula: x = ar{x} + z(S)
  3. Calculate: x10=22+(−1.2816)(5.19)x_{10} = 22 + (-1.2816)(5.19) x90=22+(1.2816)(5.19)x_{90} = 22 + (1.2816)(5.19)
  4. Subtract the results to find the interpercentile range.

Step 5

State two variables from the large data set for Beijing that are not suitable to be normally distributed.

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Answer

  1. Daily mean wind speed: This variable is often limited by a lower boundary of zero (can’t have negative speed), and tends to show skewness.
  2. Rainfall: Rainfall data is not symmetric, often showing many days with no rain leading to a highly skewed distribution.

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