Theory question 107
StatisticsThe table shows the distribution of the lengths of 20 iron rods measured in metres.
Length (m): 1.0 − 1.1, 1.2 − 1.3, 1.4 − 1.5, 1.6 − 1.7, 1.8 − 1.9
Frequency: 2, 3, 8, 5, 2
Using an assumed mean of 1.45, calculate the mean of the distribution.
Show the model answer
Model answer
Class marks 1.05, 1.25, 1.45, 1.65, 1.85; d = −0.4, −0.2, 0, 0.2, 0.4.
Σfd = −0.8 − 0.6 + 0 + 1.0 + 0.8 = 0.4; Σf = 20.
Mean = 1.45 + 0.4/20 = 1.47 m.
Explanation
Mean = A + Σfd/Σf.