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
Question 2
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
First, we calculate the interquartile range (IQR):
To find Q1 and Q3, we need the lower and upper whiskers. Given the three lowest values, the lower whisker is 7.6°C and the upper whisker can be determined based on other temperatures (not provided).
Assuming that the IQR can be calculated as follows: IQR=Q3−Q1, where we assume Q1 is around 8.1°C and Q3 might be around 22.6°C, leading to an IQR of 14.5°C.
Outliers are values that are more than 1.5 × IQR below Q1 or above Q3:
More than 1.5∗14.5=21.75 below 8.1°C or above 22.6°C
Therefore, temperature values less than -13.65°C (not applicable) or greater than 43.6°C (not applicable). Since 32.5°C does not exceed this limit, it shows no clear outliers in the shown 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
October is suggested as the month, as it typically has the coldest temperatures in Beijing, potentially leading to lower temperature outliers.
Step 3
Show that, to 3 significant figures, the standard deviation is 5.19°C.
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Answer
To find the standard deviation, we apply the formula:
S = rac{S_s}{ ext{n}}
Here, we have:
Ss=4952.906
n=184
Thus, the sample variance is calculated as follows:
s2=n−1Ss=1834952.906=27.06
Finally, the standard deviation s=27.06≈5.19 (to 3 significant figures).
Step 4
Using Simon's model, calculate the 10th to 90th interpercentile range.
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Answer
With the model T∼N(22.6,5.192):
The 10th percentile can be calculated using:
P10=μ+z⋅σ
Where z=−1.2816 (from Z-table):
P10=22.6−1.2816⋅5.19≈18.82
For the 90th percentile (z=1.2816):
P90=22.6+1.2816⋅5.19≈26.48
Thus, the interpercentile range is P90−P10≈26.48−18.82=7.66.
Step 5
State two variables from the large data set for Beijing that are not suitable to be modeled by a normal distribution. Give a reason for each answer.
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Answer
Rainfall: Rainfall data is often skewed with a large number of days with zero rainfall, making it non-normally distributed.
Daily mean wind speed: Wind speed data tends to have a lower limit (zero) and upper limits, resulting in skewness and thus inappropriate for normal modeling.
