Question

A student repeatedly measures the mass of an object using a mechanical balance and gets the following values: 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g Calculate the standard deviation of his measurements

Answer 1

Answer: 2.76 g

Explanation:

The formula to find the standard deviation:-

`\sigma=\sqrt{\frac{\sum(x_i-\overline{x})^2}{n}}`

The given data values : 560 g, 562 g, 556 g, 558 g, 560 g, 556 g, 559 g, 561 g, 565 g, 563 g.

Then,
`\overline{x}=(\sum_(i=1)^(10) x_i)/(n)\\\\\Rightarrow\ \overline{x}=(560+562+556+558+560+556+559+561+565+563)/(10)\\\\\Rightarrow\ \overline{x}=(5600)/(10)=560`

Now,
`\sum_(i=1)^(10)(x_i-\overline{x})^2=0^2+2^2+(-4)^2+(-2)^2+0^2+(-4)^2+(-1)^2+1^2+5^2+3^2\\\\\Rightarrow\ \sum_(i=1)^(10)(x_i-\overline{x})^2=76`

Then,
`\sigma=\sqrt{(76)/(10)}=√(7.6)=2.76`

Hence, the standard deviation of his measurements = 2.76 g