Question

exercise 3: length of a pencil: 12.0 cm, 12.1 cm, 12.2 cm, 12.1 a) find the average: b) find the range: c) find the random error:

Explanation:

Part a)

Step1: Sum the values

The values are \( 12.0 \, \text{cm}, 12.1 \, \text{cm}, 12.2 \, \text{cm}, 12.1 \, \text{cm} \). Let's sum them: \( 12.0 + 12.1 + 12.2 + 12.1 = 48.4 \, \text{cm} \)

Step2: Divide by number of values

There are 4 values. So average \( = \frac{48.4}{4} = 12.1 \, \text{cm} \)

Step1: Identify max and min

Max value \( = 12.2 \, \text{cm} \), Min value \( = 12.0 \, \text{cm} \)

Step2: Calculate range

Range \( = \text{Max} - \text{Min} = 12.2 - 12.0 = 0.2 \, \text{cm} \)

Step1: Recall random error formula

Random error is half of the range.

Step2: Calculate random error

Range is \( 0.2 \, \text{cm} \), so random error \( = \frac{0.2}{2} = 0.1 \, \text{cm} \)

Answer:

\( 12.1 \, \text{cm} \)

Part b)