Choose the four true statements from the following.
Options for Question 5
A )Two boxplots plotted ona commonaxis would be a good way of comparing the journey times for weekdays and weekends.
B )Boxplots would show that the weekend times are more widely spread than the weekday times.
C) Boxplots would show that the weekend times are less widely spread than the weekday times.
D )Boxplots would show that the upper quartile for weekend times is greater than the maximum for weekday times.
E) A boxplot for the weekday journey times would have the left whisker shorter than the right whisker.
F) The boxplots would show that the median for the weekday times is nearer the upper quartile than the lower quartile.
G) From these data you can reliably conclude that journeys at weekends will always take longer than journeys during the week.
H)From these data you can reliably conclude that journeys at weekends will always take less time than journeys during the week.
To determine which statements are true, we can analyze each option:
A) Two boxplots plotted on a common axis would be a good way of comparing the journey times for weekdays and weekends.
This statement is true, as a side-by-side box plot allows for a visual comparison of the distribution of journey times for weekdays and weekends.
B) Boxplots would show that the weekend times are more widely spread than the weekday times.
This statement is likely true, as the interquartile range (IQR) in a boxplot represents the spread of the data. If the IQR of the weekend times is larger than the weekday times, it indicates a wider spread.
C) Boxplots would show that the weekend times are less widely spread than the weekday times.
This statement is false, as it contradicts statement B.
D) Boxplots would show that the upper quartile for weekend times is greater than the maximum for weekday times.
This statement is false. The upper quartile of a boxplot represents the value below which 75% of the data falls. It cannot be greater than the maximum value.
E) A boxplot for the weekday journey times would have the left whisker shorter than the right whisker.
This statement is false. In a boxplot, the whiskers represent the range of the data within a certain threshold. The left whisker extends to the smallest non-outlier data point, and the right whisker to the largest non-outlier data point.
F) The boxplots would show that the median for the weekday times is nearer the upper quartile than the lower quartile.
This statement is likely true. In a boxplot, the median is represented by the horizontal line inside the box. If the median is closer to the upper quartile than the lower quartile, it suggests that the distribution is skewed towards higher values.
G) From these data you can reliably conclude that journeys at weekends will always take longer than journeys during the week.
This statement is not supported by the given information. The data only provides insights into the spread and distribution of journey times, not the specific durations.
H) From these data you can reliably conclude that journeys at weekends will always take less time than journeys during the week.
This statement is not supported by the given information. The data only provides insights into the spread and distribution of journey times, not the specific durations.
Based on the analysis, the four true statements are:
A) Two boxplots plotted on a common axis would be a good way of comparing the journey times for weekdays and weekends.
B) Boxplots would show that the weekend times are more widely spread than the weekday times.
F) The boxplots would show that the median for the weekday times is nearer the upper quartile than the lower quartile.
The remaining statements (C, D, E, G, H) are false or not supported by the given information.