Measurement, Errors, Data and Unit Conversion

Precision refers to the repeatability of the measurement. In choice B, all measurements are the same so are precise.

1 g is a thousand milligrams, so three quarters of a gram is three quarters of a thousand milligrams = 750 mg (g to mg: shift the decimal point three places to the right).

One millionth = 10−6.

A reading of 68.4 (i.e. stated to the nearest 0.1 kg) means that the actual value is between 68.35 and 68.44, so only 68.47 (which is closer to 68.5) is outside this range.

By definition, absolute error is half the smallest scale interval (0.1 in this case) above and below the measured value.

A square metre has sides that are 100 cm long, so 100 × 100 = 10,000 cm2 in a square metre. So 3400 ÷ 10,000 = 0.34.

Absolute error is plus or minus half the smallest scale interval. Two times 0.05 = 0.1, so the smallest scale interval is 0.1 of a degree which applies to the 37.8 °C value.

Mode is the most commonly occurring value. $475 appears three times so is the mode.

The term “standard” in standard deviation of a distribution of measured values means that it may be relied upon to encompass 68% of all measured values.

Normally distributed data have this predicable relationship between their mean and the spread of values around the mean.