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Statistical Software Data Analysis

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Statistical Software Data Analysis

Keira and Anahera use statistical software to investigate how long passengers wait for a city bus. The times below are a sample of 12 waits, measured in minutes. Use the data and software output to answer the questions. Give units where appropriate, and explain what the results mean in context.

Enter and check the data

The sample was collected at one stop on a weekday afternoon.

1.Before calculating statistics, Keira notices that one wait time is much larger than the others. What should she do first in the software, and why?

2.The software imports the values as text rather than numbers. Which task is most likely to be affected?

Calculating a numerical mean
Changing the spreadsheet background colour
Sorting passenger names alphabetically
Adding a title to a report

3.Calculate the median wait time from the 12 values. Show how you found it.

Read the software output

After checking the entries, the software reports the following summary.

Number of waits

Mean

11.7 min (rounded to 1 d.p.)

Median

10.5 min

Lower quartile (Q1)

8 min

Upper quartile (Q3)

13.5 min

Minimum and maximum

4 min and 28 min

4.What does the median of 10.5 minutes tell Keira about the sample of passenger waits?

5.The mean is greater than the median. Which value most likely pulls the mean upwards?

4 minutes
8 minutes
10 minutes
28 minutes

6.Find the interquartile range (IQR) using the software output. What does the IQR describe in this context?

7.Zoe says, “The mean wait is 11.7 minutes, so passengers on this route usually wait exactly 11.7 minutes.” Explain why this conclusion is not justified.

8.The software makes a histogram with a bin from 8 minutes up to, but not including, 12 minutes. How many waits belong in that bin?

9.Anahera wants to investigate whether wait times differ between morning and afternoon. What additional data should she collect, and what comparison would be useful?

10.Write a two-sentence conclusion for a passenger information report. Include at least one numerical result and one limitation of this investigation.