A botanist was interested in the average height and standard deviation of a new plant variety. The following data are the heights for a sample of n=10 plants. The average height is 11.00 cm, rounded to two places. Find the sample standard deviation, rounded to two decimal places.
9.5, 12, 11.5, 10.5, 13, 10, 11.5, 12, 10.5, 9.5
Show answer & explanation
Correct answer: B
Explanation
9.5, 12, 11.5, 10.5, 13, 10, 11.5, 12, 10.5, 9.5
Mean = 11.00 cm
(9.5 − 11)² = 2.25
(12 − 11)² = 1
(11.5 − 11)² = 0.25
(10.5 − 11)² = 0.25
(13 − 11)² = 4
(10 − 11)² = 1
(11.5 − 11)² = 0.25
(12 − 11)² = 1
(10.5 − 11)² = 0.25
(9.5 − 11)² = 2.25
Sum = 12.5
Standard Deviation -
s = √[Σ(x − x̄)² / (n − 1)]
= √(12.5 / 9)
= √1.3889
≈ 1.18 cm