Five-Number Summary worksheet

1. Five-number summary (min, Q1, median, Q3, max): 8, 21, 36, 41.5, 50

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

   $8\text{,}8\text{,}13\text{,}29\text{,}\text{…}\text{,}48\text{,}50$

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

   $\mathrm{median}$$=36$

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}$$=13+0.5\times \left(29-13\right)$$=21$

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}$$=38+0.5\times \left(45-38\right)$$=41.5$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=41.5-21$$=20.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{8, 21, 36, 41.5, 50}$

2. Five-number summary (min, Q1, median, Q3, max): 7, 22, 45, 48, 56

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

   $7\text{,}7\text{,}22\text{,}34\text{,}\text{…}\text{,}50\text{,}56$

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

   $\mathrm{median}$$=45$

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}7\text{,}7\text{,}22\text{,}34\text{,}42$$=22$

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

   $\mathrm{Q3}\text{= median of}45\text{,}46\text{,}48\text{,}50\text{,}56$$=48$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=48-22$$=26$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{7, 22, 45, 48, 56}$

3. Five-number summary (min, Q1, median, Q3, max): 4, 18, 40, 46.5, 65

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

   $4\text{,}7\text{,}14\text{,}22\text{,}\text{…}\text{,}50\text{,}65$

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

   $\mathrm{median}$$=40$

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}$$=14+0.5\times \left(22-14\right)$$=18$

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}$$=46+0.5\times \left(47-46\right)$$=46.5$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=46.5-18$$=28.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{4, 18, 40, 46.5, 65}$

4. Five-number summary (min, Q1, median, Q3, max): 6, 15, 40, 43, 49

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

   $6\text{,}7\text{,}15\text{,}36\text{,}\text{…}\text{,}47\text{,}49$

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

   $\mathrm{median}$$=40$

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}6\text{,}7\text{,}15\text{,}36\text{,}39$$=15$

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

   $\mathrm{Q3}\text{= median of}41\text{,}42\text{,}43\text{,}47\text{,}49$$=43$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=43-15$$=28$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{6, 15, 40, 43, 49}$

5. Five-number summary (min, Q1, median, Q3, max): 4, 25, 38, 42.5, 48

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

   $4\text{,}5\text{,}16\text{,}34\text{,}\text{…}\text{,}48\text{,}48$

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

   $\mathrm{median}$$=38$

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}$$=16+0.5\times \left(34-16\right)$$=25$

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}$$=40+0.5\times \left(45-40\right)$$=42.5$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=42.5-25$$=17.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{4, 25, 38, 42.5, 48}$

6. Five-number summary (min, Q1, median, Q3, max): 5, 23, 34, 43, 60

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

   $5\text{,}8\text{,}18\text{,}28\text{,}\text{…}\text{,}55\text{,}60$

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

   $\mathrm{median}$$=34$

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}$$=18+0.5\times \left(28-18\right)$$=23$

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}$$=41+0.5\times \left(45-41\right)$$=43$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=43-23$$=20$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{5, 23, 34, 43, 60}$

7. Five-number summary (min, Q1, median, Q3, max): 4, 25, 42, 44.5, 50

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

   $4\text{,}6\text{,}18\text{,}32\text{,}\text{…}\text{,}47\text{,}50$

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

   $\mathrm{median}$$=42$

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}$$=18+0.5\times \left(32-18\right)$$=25$

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}$$=44+0.5\times \left(45-44\right)$$=44.5$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=44.5-25$$=19.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{4, 25, 42, 44.5, 50}$

8. Five-number summary (min, Q1, median, Q3, max): 4, 25.5, 42, 47, 50

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

   $4\text{,}8\text{,}15\text{,}36\text{,}\text{…}\text{,}50\text{,}50$

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

   $\mathrm{median}$$=42$

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}$$=15+0.5\times \left(36-15\right)$$=25.5$

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}$$=46+0.5\times \left(48-46\right)$$=47$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=47-25.5$$=21.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{4, 25.5, 42, 47, 50}$

9. Five-number summary (min, Q1, median, Q3, max): 7, 25.5, 38, 42, 50

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

   $7\text{,}7\text{,}21\text{,}30\text{,}\text{…}\text{,}50\text{,}50$

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

   $\mathrm{median}$$=38$

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}$$=21+0.5\times \left(30-21\right)$$=25.5$

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}$$=40+0.5\times \left(44-40\right)$$=42$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=42-25.5$$=16.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{7, 25.5, 38, 42, 50}$

10. Five-number summary (min, Q1, median, Q3, max): 4, 20.5, 38, 45, 60

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

   $4\text{,}7\text{,}15\text{,}26\text{,}\text{…}\text{,}55\text{,}60$

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

   $\mathrm{median}$$=38$

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}$$=15+0.5\times \left(26-15\right)$$=20.5$

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}$$=45+0.5\times \left(45-45\right)$$=45$

5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

   $\mathrm{IQR}$$=45-20.5$$=24.5$

6. Put the minimum, Q1, median, Q3 and maximum together

   $\text{4, 20.5, 38, 45, 60}$