7.06 Outliers and measures of center
Identify the outlier in the following data sets:
5, \,6, \,7, \,8, \,9, \,9, \,18
59, \,61, \,63, \,70, \,73, \,76, \,113
10, \,7, \,6, \,8, \,1, \,10, \,6
73, \,65, \,72, \,68, \,74, \,57, \,121
Identify the outlier(s) in the following data sets:
The scores achieved by students in a class on a particular math exam were:
66, \,74, \,62, \,64, \,60, \,24, \,68, \,67, \,70, \,61, \,58, \,57, \,73, \,71, \,75, \,63Rochelle recorded the heights (in centimeters) of all the students in her class:
148, \,153, \,137, \,142, \,140, \,146, \,136, \,143, \,135, \,144, \,189, \,138, \,149, \,139, \,145, \,150
Frank has just finished a successful cricket season. Over the course of the season, he managed to make the following number of runs in each of his innings:
50, \,53, \,54, \,8, \,51, \,46, \,48, \,61, \,56, \,49, \,55, \,59, \,44, \,104
Consider the following set of data:27,\, 50,\, 24,\, 37,\, 47,\, 41,\, 27,\, 126,\, 44,\, 27
Find the following:
Mean
Median
Mode
Range
Which data value is an outlier?
Find the following after removing the outlier:
Mean
Median
Mode
Range
Compare the the mean, meadian, mode and range before and after removing the outlier.
When an outlier is removed from a data set, describe the effect on the following:
Consider the following frequency table:
If the outlier is removed what is the new mode?
| Weight in kilograms | Frequency |
|---|---|
| 14 | 1 |
| 15 | 0 |
| 16 | 0 |
| 17 | 3 |
| 18 | 6 |
| 19 | 4 |
| 20 | 2 |
Consider the following frequency table:
If the outlier is removed what is the new mean? Round your answer to two decimal places if needed.
| Weight in kilograms | Frequency |
|---|---|
| 12 | 2 |
| 13 | 5 |
| 14 | 1 |
| 15 | 2 |
| 16 | 0 |
| 17 | 0 |
| 18 | 1 |
Which measure of center would be best for describing the following data sets?
State the most appropriate measure of center for the following scenarios:
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
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 center most accurately describes the center of this data set? 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
Determine the mean number of times a speed camera issued a fine in that month. Round your answer to one decimal place.
Determine the median number of times a speed camera issued a fine in that month. Round your answer to one decimal place.
Which measure is most representative of the number of fines issued by each speed camera in one month?
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. What statement should she make?