Limitations of Measures of Centre and Spread
Interactive practice questions
A journalist wanted to report on road speed cameras being used as revenue raisers. She obtained data that showed the number of times $20$20 speed cameras issued a fine to motorists in one month. The results were:
$101,102,115,115,121,124,127,128,130,130,143,143,146,162,162,163,178,183,194,977$101,102,115,115,121,124,127,128,130,130,143,143,146,162,162,163,178,183,194,977
Determine the mean number of times a speed camera issued a fine in that month. Give your answer correct to one decimal place.
Determine the median number of times a speed camera issued a fine in that month. Give your answer correct to one decimal place.
Which measure is most representative of the number of fines issued by each speed camera in one month?
the mean
the median
Which score causes the mean to be much greater than the median?
The journalist wants to give the impression that speed cameras are just being used to raise revenue. Which statement should she make?
A sample of $20$20 speed cameras found that the median number of fines in one month was $136.5$136.5.
A sample of $20$20 speed cameras found that, on average, $182.2$182.2 fines were issued in one month.
Teachers at a school suspected that the participation rate of students aged 13 to 15 in extra curricular activities was low compared to other ages. They asked a sample of students if they had participated in any activities in the last year, and recorded their ages. The results are presented in the dot plot.
In a countrywide census, information is gathered to determine the make up of the population.
In a study of home affordability, a sample of $10$10 families were asked what percentage of their household income goes towards mortgage repayments (to the nearest $5%$5%). The results were:
$35%$35%, $40%$40%, $10%$10%, $30%$30%, $30%$30%, $15%$15%, $35%$35%, $30%$30%, $35%$35%, $35%$35%