Percentile worksheet

1. Percentile rank: 50%

1. Put the 5 values in order from smallest to largest

   $20\text{,}22\text{,}30\text{,}32\text{,}50$

2. Count the values below 30 (B) and the values equal to it (E)

   $B=2\text{,}E=1$

3. Add the values below plus half of the ties, so a tied value lands in the middle of its group. Then divide by the count and multiply by 100

   $\mathrm{PR}$$=\frac{2+0.5\times 1}{5}\times 100$$=\mathrm{50\%}$

2. Value at the 45th percentile: 28.8

1. Put the 5 values in order from smallest to largest

   $18\text{,}24\text{,}30\text{,}30\text{,}41$

2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

   $r$$=1+\left(5-1\right)\times \frac{45}{100}$$=2.8$

3. r falls between two spots, so start at value number 2 and move 0.8 of the way to value number 3

   $\mathrm{value}$$=24+0.8\times \left(30-24\right)$$=28.8$

3. Percentile rank: 60%

1. Put the 5 values in order from smallest to largest

   $18\text{,}28\text{,}30\text{,}55\text{,}56$

2. Count the values below 35 (B) and the values equal to it (E)

   $B=3\text{,}E=0$

3. Add the values below plus half of the ties, so a tied value lands in the middle of its group. Then divide by the count and multiply by 100

   $\mathrm{PR}$$=\frac{3+0.5\times 0}{5}\times 100$$=\mathrm{60\%}$

4. Value at the 38th percentile: 28.72

1. Put the 5 values in order from smallest to largest

   $16\text{,}23\text{,}34\text{,}35\text{,}40$

2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

   $r$$=1+\left(5-1\right)\times \frac{38}{100}$$=2.52$

3. r falls between two spots, so start at value number 2 and move 0.52 of the way to value number 3

   $\mathrm{value}$$=23+0.52\times \left(34-23\right)$$=28.72$

5. Value at the 50th percentile: 35

1. Put the 5 values in order from smallest to largest

   $15\text{,}20\text{,}35\text{,}40\text{,}50$

2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

   $r$$=1+\left(5-1\right)\times \frac{50}{100}$$=3$

3. r is a whole number, so the percentile is value number 3 in the sorted list

   $\mathrm{value}$$=35$

6. Value at the 40th percentile: 27.6

1. Put the 5 values in order from smallest to largest

   $14\text{,}18\text{,}34\text{,}39\text{,}60$

2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

   $r$$=1+\left(5-1\right)\times \frac{40}{100}$$=2.6$

3. r falls between two spots, so start at value number 2 and move 0.6 of the way to value number 3

   $\mathrm{value}$$=18+0.6\times \left(34-18\right)$$=27.6$

7. Value at the 42nd percentile: 23.76

1. Put the 5 values in order from smallest to largest

   $13\text{,}19\text{,}26\text{,}44\text{,}45$

2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

   $r$$=1+\left(5-1\right)\times \frac{42}{100}$$=2.68$

3. r falls between two spots, so start at value number 2 and move 0.68 of the way to value number 3

   $\mathrm{value}$$=19+0.68\times \left(26-19\right)$$=23.76$

8. Percentile rank: 80%

1. Put the 5 values in order from smallest to largest

   $11\text{,}20\text{,}32\text{,}34\text{,}45$

2. Count the values below 39 (B) and the values equal to it (E)

   $B=4\text{,}E=0$

3. Add the values below plus half of the ties, so a tied value lands in the middle of its group. Then divide by the count and multiply by 100

   $\mathrm{PR}$$=\frac{4+0.5\times 0}{5}\times 100$$=\mathrm{80\%}$

9. Value at the 36th percentile: 27.68

1. Put the 5 values in order from smallest to largest

   $14\text{,}18\text{,}40\text{,}40\text{,}45$

2. Find the rank position r, the spot in the sorted list where the percentile falls. Rank 1 is the smallest value

   $r$$=1+\left(5-1\right)\times \frac{36}{100}$$=2.44$

3. r falls between two spots, so start at value number 2 and move 0.44 of the way to value number 3

   $\mathrm{value}$$=18+0.44\times \left(40-18\right)$$=27.68$

10. Percentile rank: 40%

1. Put the 5 values in order from smallest to largest

   $13\text{,}15\text{,}45\text{,}45\text{,}50$

2. Count the values below 24 (B) and the values equal to it (E)

   $B=2\text{,}E=0$

3. Add the values below plus half of the ties, so a tied value lands in the middle of its group. Then divide by the count and multiply by 100

   $\mathrm{PR}$$=\frac{2+0.5\times 0}{5}\times 100$$=\mathrm{40\%}$