Identifying Outliers

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Class:

Date:

Show your work for each problem.

1.
What is an outlier?
1. a)The difference between Q3 and Q1
2. b)The middle value of the ordered data
3. c)A value unusually far from the rest of the data
4. d)The value that appears most often
2.
A data set has $Q_1 = 10$ and $Q_3 = 18$ . What is $1.5 \times \text{IQR}$ ?
3.
The lower fence of a data set is $12$ and the upper fence is $36$ . Which value is an outlier?
1. a)35
2. b)14
3. c)40
4. d)12
4.
A data set has $Q_1 = 40$ and $Q_3 = 50$ . What is the upper fence?
5.
The data set $10, 11, 12, 13, 14$ gets one new value: $90$ . Which measure changes the least?
1. a)The median
2. b)The mean
3. c)The range
4. d)The maximum
6.
A data set has $Q_1 = 24$ and $Q_3 = 36$ . What is the lower fence?
7.
Find the outlier in $10, 12, 13, 15, 16, 18, 19, 20, 35$ .
8.
Find the mean of $5, 6, 7, 8, 30$ . (The median is $7$ .)
9.
Check the data set $2, 14, 15, 16, 17, 18, 19, 20$ for a low outlier.
10.
In a box plot, the whiskers go from $15$ to $42$ and there is a separate dot at $70$ . What does the dot mean?
1. a)70 is where the upper whisker should end
2. b)70 is the median
3. c)70 is an outlier: it lies above the upper fence
4. d)70 is the third quartile Q3
11.
The data set $4, 6, 7, 8, 10$ gets one more value: $49$ . How do the mean and the median change?
12.
For $3, 5, 6, 7, 8, 9, 31$ : show that $31$ is an outlier and compare the range with and without it.
13.
Test scores: $60, 65, 70, 72, 75, 78, 80, 95$ . Is the top score $95$ an outlier?
14.
Find the lower fence of $1, 8, 9, 10, 11, 12, 13$ .
15.
How many outliers does $1, 20, 22, 23, 24, 25, 26, 27, 28, 50$ have?
16.
A runner's last 7 times for 5 km (minutes): $24, 25, 25, 26, 26, 27, 52$ . On the 52-minute day she sprained her ankle and walked home. The upper fence is $30$ . What is the best way to describe her usual time?
1. a)Use the mean of all 7 times
2. b)Use the range of all 7 times
3. c)Use the median (26 minutes), or leave out 52 and say why
4. d)Change 52 to 25 so it fits the others
17.
Heights in cm: $150, 155, 158, 160, 162, 1600$ . The $1600$ is a typo for $160$ . Compare the mean and median before and after correcting it.
18.
Draw the box plot of $3, 10, 11, 12, 13, 14, 15, 16, 30$ : find the fences and where the upper whisker ends.