Question

an objects length is measured three times (2.10 cm, 2.20 cm, and 2.60 cm). calculate the standard deviation.
a 0.170 cm
b 0.265 cm
c 0.503 cm
d 2.30 cm

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{2.10 + 2.20+2.60}{3}=\frac{6.9}{3}=2.3$ cm.

Step2: Calculate the squared differences

For \(x_1 = 2.10\): \((2.10 - 2.3)^2=(- 0.2)^2 = 0.04\)
For \(x_2 = 2.20\): \((2.20 - 2.3)^2=(-0.1)^2 = 0.01\)
For \(x_3 = 2.60\): \((2.60 - 2.3)^2=(0.3)^2 = 0.09\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{0.04 + 0.01+0.09}{3 - 1}=\frac{0.14}{2}=0.07\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{0.07}\approx0.265\) cm

Answer:

B. \(0.265\) cm