A researcher collected data on the growth of a specific bacteria strain in a new nutrient medium. The following table shows the colony diameter (in mm) for a sample of n=10 colonies after 24 hours. The average colony diameter is 5.65 mm, rounded to two places. Find the sample standard deviation, rounded to two decimal places.
| 4.5 | 6 | 6.5 | 5 | 7 | 4 | 6.5 | 7 | 5.5 | 4.5 |
Show answer & explanation
Correct answer: C
Explanation
Data = 4.5, 6, 6.5, 5, 7, 4, 6.5, 7, 5.5, 4.5
n = 10, Mean = 5.65
(4.5−5.65)² = 1.3225
(6−5.65)² = 0.1225
(6.5−5.65)² = 0.7225
(5−5.65)² = 0.4225
(7−5.65)² = 1.8225
(4−5.65)² = 2.7225
(6.5−5.65)² = 0.7225
(7−5.65)² = 1.8225
(5.5−5.65)² = 0.0225
(4.5−5.65)² = 1.3225
Sum = 10.98
Variance = 10.98 ÷ 9 = 1.22
Standard Deviation = √1.22 = 1.11