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The table below is an extract from the Large Data Set - AQA - A-Level Maths Mechanics - Question 13 - 2021 - Paper 3
Question 13
The table below is an extract from the Large Data Set. | Propulsion Type | Region | Engine Size | Mass | CO2 | Particulate Emissions | |----------------|------... show full transcript
Worked Solution & Example Answer:The table below is an extract from the Large Data Set - AQA - A-Level Maths Mechanics - Question 13 - 2021 - Paper 3
Step 1
Calculate the mean and standard deviation of CO2 emissions in the table.
Answer
To calculate the mean CO2 emissions, sum all the CO2 values from the table and divide by the total number of entries.
The CO2 values are: 154, 138, 138, 159, 130, 146, 154, 192, 122, 175, 140, 146.
Calculating the sum:
The number of entries is 12.
Now, calculate the mean:
ext{Mean} = rac{1844}{12} \\ ext{Mean} hickapprox 153.67
Next, to find the standard deviation, use the formula:
ext{Standard Deviation} = rac{1}{N} imes igg( ext{Sum of } (x_i - ext{mean})^2 igg)^{0.5}
After evaluating this based on the individual differences, we will arrive at a standard deviation of approximately . Hence, the mean and standard deviation are:
Mean:
Standard Deviation:
Step 2
Any value more than 2 standard deviations from the mean can be identified as an outlier.
Answer
We can determine the outlier boundaries by calculating:
Substituting known values into the calculations:
Now we check the CO2 emissions:
The outliers will be any CO2 values above 189.27 or below 118.07. The only CO2 emission value that exceeds the upper boundary is 192. Therefore:
- 192 is classified as an outlier.
Step 3
Maria claims that the last line in the table must contain two errors.
Answer
Maria's claim regarding the last line can be analyzed based on the provided data.
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The CO2 value of 0 is indeed an error because every car has a mass or there is a driver mass which should not allow for a CO2 emission of 0. Thus, it indicates a data entry error.
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The blank cell may not be an error as the Large Data Set only records emissions. Since the last row holds a valid CO2 emission when corrected, it could be justified that the record is appropriate as per the dataset guidelines.
Therefore, while the CO2 value is erroneous, the absence of mass information does not constitute an error in the dataset context.