Outlier worksheet

1. Outliers: 1, 55

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}11\text{,}12\text{,}13\text{,}\text{…}\text{,}16\text{,}55$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. For Q1, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.25 = 3.5. That falls between value number 3 and number 4, so go 0.5 of the way from one to the other

   $\mathrm{Q1}$$=12+0.5\times \left(13-12\right)$$=12.5$

4. For Q3, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.75 = 8.5. That falls between value number 8 and number 9, so go 0.5 of the way from one to the other

   $\mathrm{Q3}$$=16+0.5\times \left(16-16\right)$$=16$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=16-12.5$$=3.5$

6. Step k = 1.2 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=12.5-1.2\times 3.5$$=8.3$

7. Step k = 1.2 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=16+1.2\times 3.5$$=20.2$

8. Step 4 IQRs out for the outer fences, which mark the extreme outliers

   $12.5-4\times 3.5\text{=}\mathrm{-1.5}\text{and}16+4\times 3.5\text{=}30$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 55}$

2. Outliers: 1, 10, 44

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}10\text{,}16\text{,}17\text{,}\text{…}\text{,}20\text{,}44$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=18$

3. Q1, the lower quartile, is the middle of the lower half. The overall median is left out of both halves

   $\mathrm{Q1}\text{= median of}1\text{,}10\text{,}16\text{,}17\text{,}18$$=16$

4. Q3, the upper quartile, is the middle of the upper half

   $\mathrm{Q3}\text{= median of}18\text{,}18\text{,}20\text{,}20\text{,}44$$=20$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=20-16$$=4$

6. Step k = 1.4 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=16-1.4\times 4$$=10.4$

7. Step k = 1.4 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=20+1.4\times 4$$=25.6$

8. Step 3 IQRs out for the outer fences, which mark the extreme outliers

   $16-3\times 4\text{=}4\text{and}20+3\times 4\text{=}32$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 10, 44}$

3. Outliers: 1, 44

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}12\text{,}13\text{,}14\text{,}\text{…}\text{,}18\text{,}44$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. For Q1, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.25 = 3.5. That falls between value number 3 and number 4, so go 0.5 of the way from one to the other

   $\mathrm{Q1}$$=13+0.5\times \left(14-13\right)$$=13.5$

4. For Q3, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.75 = 8.5. That falls between value number 8 and number 9, so go 0.5 of the way from one to the other

   $\mathrm{Q3}$$=16+0.5\times \left(17-16\right)$$=16.5$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=16.5-13.5$$=3$

6. Step k = 0.9 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=13.5-0.9\times 3$$=10.8$

7. Step k = 0.9 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=16.5+0.9\times 3$$=19.2$

8. Step 4 IQRs out for the outer fences, which mark the extreme outliers

   $13.5-4\times 3\text{=}1.5\text{and}16.5+4\times 3\text{=}28.5$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 44}$

4. Outliers: 1, 44

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}12\text{,}13\text{,}14\text{,}\text{…}\text{,}18\text{,}44$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. Q1, the lower quartile, is the middle of the lower half. The overall median is left out of both halves

   $\mathrm{Q1}\text{= median of}1\text{,}12\text{,}13\text{,}14\text{,}15$$=13$

4. Q3, the upper quartile, is the middle of the upper half

   $\mathrm{Q3}\text{= median of}16\text{,}16\text{,}17\text{,}18\text{,}44$$=17$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=17-13$$=4$

6. Step k = 1.7 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=13-1.7\times 4$$=6.2$

7. Step k = 1.7 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=17+1.7\times 4$$=23.8$

8. Step 3 IQRs out for the outer fences, which mark the extreme outliers

   $13-3\times 4\text{=}1\text{and}17+3\times 4\text{=}29$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 44}$

5. Outliers: 1, 42

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}12\text{,}12\text{,}12\text{,}\text{…}\text{,}18\text{,}42$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=16$

3. For Q1, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.25 = 3.5. That falls between value number 3 and number 4, so go 0.5 of the way from one to the other

   $\mathrm{Q1}$$=12+0.5\times \left(12-12\right)$$=12$

4. For Q3, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.75 = 8.5. That falls between value number 8 and number 9, so go 0.5 of the way from one to the other

   $\mathrm{Q3}$$=16+0.5\times \left(18-16\right)$$=17$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=17-12$$=5$

6. Step k = 1.7 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=12-1.7\times 5$$=3.5$

7. Step k = 1.7 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=17+1.7\times 5$$=25.5$

8. Step 3 IQRs out for the outer fences, which mark the extreme outliers

   $12-3\times 5\text{=}\mathrm{-3}\text{and}17+3\times 5\text{=}32$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 42}$

6. Outlier: 43

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $2\text{,}11\text{,}12\text{,}12\text{,}\text{…}\text{,}22\text{,}43$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=14$

3. Q1, the lower quartile, is the middle of the lower half. The overall median is left out of both halves

   $\mathrm{Q1}\text{= median of}2\text{,}11\text{,}12\text{,}12\text{,}13$$=12$

4. Q3, the upper quartile, is the middle of the upper half

   $\mathrm{Q3}\text{= median of}15\text{,}15\text{,}20\text{,}22\text{,}43$$=20$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=20-12$$=8$

6. Step k = 1.8 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=12-1.8\times 8$$=\mathrm{-2.4}$

7. Step k = 1.8 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=20+1.8\times 8$$=34.4$

8. Step 3 IQRs out for the outer fences, which mark the extreme outliers

   $12-3\times 8\text{=}\mathrm{-12}\text{and}20+3\times 8\text{=}44$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{43}$

7. Outlier: 40

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}11\text{,}11\text{,}13\text{,}\text{…}\text{,}20\text{,}40$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. Q1, the lower quartile, is the middle of the lower half. The overall median is left out of both halves

   $\mathrm{Q1}\text{= median of}1\text{,}11\text{,}11\text{,}13\text{,}13$$=11$

4. Q3, the upper quartile, is the middle of the upper half

   $\mathrm{Q3}\text{= median of}16\text{,}16\text{,}20\text{,}20\text{,}40$$=20$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=20-11$$=9$

6. Step k = 1.3 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=11-1.3\times 9$$=\mathrm{-0.7}$

7. Step k = 1.3 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=20+1.3\times 9$$=31.7$

8. Step 3 IQRs out for the outer fences, which mark the extreme outliers

   $11-3\times 9\text{=}\mathrm{-16}\text{and}20+3\times 9\text{=}47$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{40}$

8. Outliers: 1, 44

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}12\text{,}13\text{,}14\text{,}\text{…}\text{,}18\text{,}44$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. For Q1, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.25 = 3.5. That falls between value number 3 and number 4, so go 0.5 of the way from one to the other

   $\mathrm{Q1}$$=13+0.5\times \left(14-13\right)$$=13.5$

4. For Q3, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.75 = 8.5. That falls between value number 8 and number 9, so go 0.5 of the way from one to the other

   $\mathrm{Q3}$$=16+0.5\times \left(17-16\right)$$=16.5$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=16.5-13.5$$=3$

6. Step k = 1.5 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=13.5-1.5\times 3$$=9$

7. Step k = 1.5 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=16.5+1.5\times 3$$=21$

8. Step 4 IQRs out for the outer fences, which mark the extreme outliers

   $13.5-4\times 3\text{=}1.5\text{and}16.5+4\times 3\text{=}28.5$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 44}$

9. Outliers: 1, 44

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}12\text{,}13\text{,}14\text{,}\text{…}\text{,}18\text{,}44$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. For Q1, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.25 = 3.5. That falls between value number 3 and number 4, so go 0.5 of the way from one to the other

   $\mathrm{Q1}$$=13+0.5\times \left(14-13\right)$$=13.5$

4. For Q3, find its position (rank) in the sorted list, r = 1 + (n − 1) × 0.75 = 8.5. That falls between value number 8 and number 9, so go 0.5 of the way from one to the other

   $\mathrm{Q3}$$=16+0.5\times \left(17-16\right)$$=16.5$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=16.5-13.5$$=3$

6. Step k = 1.4 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=13.5-1.4\times 3$$=9.3$

7. Step k = 1.4 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=16.5+1.4\times 3$$=20.7$

8. Step 4 IQRs out for the outer fences, which mark the extreme outliers

   $13.5-4\times 3\text{=}1.5\text{and}16.5+4\times 3\text{=}28.5$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 44}$

10. Outliers: 1, 44

1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

   $1\text{,}12\text{,}13\text{,}14\text{,}\text{…}\text{,}18\text{,}44$

2. The median is the middle value, with half the data on each side

   $\mathrm{median}$$=15$

3. Q1, the lower quartile, is the middle of the lower half. The overall median is left out of both halves

   $\mathrm{Q1}\text{= median of}1\text{,}12\text{,}13\text{,}14\text{,}15$$=13$

4. Q3, the upper quartile, is the middle of the upper half

   $\mathrm{Q3}\text{= median of}16\text{,}16\text{,}17\text{,}18\text{,}44$$=17$

5. Subtract Q1 from Q3 to get the IQR, the spread of the middle half of your data

   $\mathrm{IQR}$$=17-13$$=4$

6. Step k = 1.5 IQRs below Q1 to set the lower fence; anything under it is unusually low

   $\text{lower fence}$$=13-1.5\times 4$$=7$

7. Step k = 1.5 IQRs above Q3 to set the upper fence; anything over it is unusually high

   $\text{upper fence}$$=17+1.5\times 4$$=23$

8. Step 3 IQRs out for the outer fences, which mark the extreme outliers

   $13-3\times 4\text{=}1\text{and}17+3\times 4\text{=}29$

9. List every value below the lower fence or above the upper fence

   $\text{Outliers:}\text{1, 44}$