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Charlie is studying the time it takes members of his company to travel to the office - Edexcel - A-Level Maths Mechanics - Question 4 - 2018 - Paper 1
Question 4
Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08:40 to 08:50 one morning and asks wo... show full transcript
Worked Solution & Example Answer:Charlie is studying the time it takes members of his company to travel to the office - Edexcel - A-Level Maths Mechanics - Question 4 - 2018 - Paper 1
Step 1
Step 2
State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.
Answer
An alternative non-random sampling method could be convenience sampling, where Charlie could choose workers who are readily available at the time, potentially by standing in areas where many employees congregate.
Step 3
Step 4
Step 5
Calculate the mean and the standard deviation for these data.
Answer
To calculate the mean, we use the formula:
ar{x} = rac{ ext{Total sum of all data}}{ ext{Number of data points}} = rac{4133}{95} ext{ which gives approximately } 43.5.
For standard deviation, the formula is:
s = rac{ ext{sqrt}igg{ rac{ ext{Sum of squares} - n(ar{x})^2}{n-1}igg{}}} where
ext{Sum of squares} = 202294, n = 95, ext{ and } ar{x} ext{ is the mean. The calculated standard deviation is } 15.4.
Step 6
State, giving a reason, whether you would recommend using the mean and standard deviation or the median and interquartile range to describe the data.
Answer
Due to the presence of outliers or skewness in the data, it is advisable to use the median and interquartile range (IQR) as they are more robust measures of central tendency and variability.
Step 7
Explain which two values Taruni must have changed and whether each of these values has increased or decreased.
Answer
The two values Taruni must have changed are the mean and standard deviation. Given that Rana’s journey decreased significantly and David’s also decreased, it is likely that the mean has decreased, affecting the overall journey times reported. Additionally, the standard deviation is also likely to decrease as the range of values narrows.