For each of the following data sets:
Are there any repeated values?
Are there any outliers?
Which measure of centre would be best for the data set?
State the most appropriate measure of centre for the following scenarios:
For a particular street in Sydney, house prices for houses sold in the last 36 months (in 1000's) were given:
920,\, 920,\, 709,\, 694,\, 667,\, 657,\, 630,\, 610,\, 584,\, 567,\, 555
The number of animal races that were won by a trainer over the years shown are listed in the table:
| Year | 2003 | 2004 | 2005 | 2006 | 2007 |
|---|---|---|---|---|---|
| Races won | 116 | 105 | 102 | 108 | 113 |
The number of minutes spent studying by each member of a group of students is given:
85,\, 85,\, 95,\, 70,\, 60,\, 70,\, 105
A netball team has so far played 8 games in the season. Their final score in each game is given:
36,\, 46,\, 49,\, 40,\, 52,\, 44,\, 39,\, 37
The number of songs Oprah has downloaded in each of the last seven months is given:
6,\, 12,\, 18,\, 9,\, 0,\, 3,\, 15
The selling price of recently sold houses is given below:
\$760\,000,\, \$650\,000,\, \$810\,000,\, \$780\,000,\, \$760\,000,\, \$590\,000,\, \$1\,360\,000
Find the mean selling price. Round your answer to the nearest thousand dollars.
Find the median selling price.
Identify the outlier.
Recalculate the mean selling price excluding the outlier.
Recalculate the median selling price excluding the outlier.
Which measure of centre is not affected when the outlier is removed, mean or median?
Which measure of centre best represents the typical selling price of recently sold houses?
The weight of fish caught in a "weigh and release" fishing competition, in kilograms are given below:
12.5,\, 15.1,\, 13,\, 14.2,\, 14.5,\, 14.9,\, 12.5,\, 14.3,\, 1.5
Find the mean weight.
Find the median weight.
Recalculate the mean weight excluding the outlier.
Recalculate the median weight excluding the outlier.
Which measure of centre best identifies the typical fish weight? Explain your answer.
Consider the histogram shown. Which measure(s) of centre best represents the centre of the data set? Explain your answer.
Carl has been recording his spelling test scores for the past semester. His scores were:14,\, 16,\, 2,\, 15,\, 15,\, 16,\, 15
Calculate the median of Carl's scores.
Calculate the mean of Carl's scores, to two decimal places.
Which measure of centre most accurately describes the centre of this data set? Explain your answer.
The salaries of part-time employees at a company are given in the dot plot below. Which measure of centre best reflects the typical wage of a part-time employee? Explain your answer.
The age of students that participated in extra-curricular activities were recorded, and their results are presented in the dot plot below:
Find the mean age of participation among the sample of students.
Find the median age of participation among the sample of students.
By looking at the dot plot, are the mean and median representative measures for the age of the typical student who participates in activities? Explain your answer.
A journalist wanted to report on road speed cameras being used as revenue raisers. She obtained data that showed the number of times 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
The journalist wants to give the impression that speed cameras are just being used to raise revenue. Which measure of centre should she use in her article? Explain your answer.