Lesson Worksheet: Outliers of a Data Set Mathematics • 8th Grade

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In this worksheet, we will practice identifying outliers from a data set.

Q1:

The table below shows the number of messages exchanged on the smart phones of 14 students over a single month. The data have also been plotted in a dot plot.

Are there any outliers in this data set? If so, specify the value or values of these outliers.

AThere is one outlier in the data: 9,754.
BThere is one outlier in the data: 4,542.
CThere are two outliers in the data: 2,830 and 9,754.
DThere is one outlier in the data: 2,830.
EThere are no outliers in the data.

Q2:

Which of the statements is correct for the distribution represented by the diagram?

AThe distribution has a peak at 22.
BThe distribution has a gap from 21 to 29.
CThe distribution has an outlier at 6.
DThe distribution is symmetric.
EThe distribution has a cluster from 7 to 20.

Q3:

The bar graph shows the prices of six different kitchen gadgets. Identify the outlier, and then find the mean of the data if the outlier is not included.

A$22.00, $150.17
B$197.00, $169.00
C$22.00, $146.50
D$22.00, $175.80
E$197.00, $140.80

Q4:

The data in the table below is the average recorded speed, in miles per hour, of the first serve of the top 10 tennis players in the world.

Average Speeds of the First Serve of the Top Ten Tennis Players (mph)
126	115	99	136	105
138	121	1,025	118	124

Calculate the mean first-serve speed in miles per hour approximated to 1 decimal place.

Recalculate the mean first-serve speed without the data point 1,025 mph, approximated to 1 decimal place.

By comparing the means you found in the first two parts of the question, make a conclusion about the validity of the 1,025 mph data point.

AThe recorded speed of 1,025 mph is very important for calculating the mean of the first-serve speed, and we can not remove it from the data set.
BThe inclusion or omission of the data point 1,025 mph drastically alters the mean of the data set because it is an extreme outlier. Physical intuition tells us that this recorded speed is probably an error.

Q5:

The table shows the heights of the tallest buildings in a city. Find, if there are any, the outliers of the data.

607	630	762	685	714	561
678	662	550	901	502	725

AThe outlier is 901 .
BThe outlier is 502 .
CThere are no outliers.
DThe outliers are 502 and 901 .

Q6:

True or False: If the numbers of games won by 12 teams in the national league is 11, 5, 6, 6, 9, 10, 19, 14, 11, 9, 9, and 6, then 19 is an outlier of the data.

ATrue
BFalse

Q7:

The table below shows the height (in centimeters) of 10 boys of the same age.

97	100	130	90	95
102	70	92	91	85

Using the standard deviation rule, identify the outlier (or outliers) approximated to one decimal place, if any.

Q8:

The table below shows the income (in thousands of British pounds) of 12 households from a neighborhood.

4.7	18.3	19.2	20.2	24.5	27.5
29.7	35.4	35.7	36.1	38.4	50.1

Using the 2-standard deviation rule, identify the outlier (or outliers), if any.

Using the 1.5 IQR rule, identify the outlier (or outliers), if any.

A50‎ ‎100 pounds
B4‎ ‎700 pounds
CNone
D4‎ ‎700 pounds and 50‎ ‎100 pounds

Q9:

Determine the outlier of the following data: 16, 16, 15, 18, 15, 15, 56.

Q10:

Find all possible outliers for the following set of data: 108, 31, 75, 87, 79, 88, 89, 118, 51, 89, 174, 95, 51, 70, and 73.

A174
B31
C70
D31, 174
EThere are no outliers.

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