Question

From the frequency distribution table below calculate;
i. The harmonic mean
ii. The geometric mean
iii. The mode
Class 25-29 30-34 35-39 40-44 45-49 50-54
Frequency 3 9 13 10 7 2

Answer 1

Answer on Question #63553 – Math – Statistics and Probability Question

From the frequency distribution table below calculate:

i) The harmonic mean

ii) The geometric mean

iii) The mode

Solution

i)

The harmonic mean is $H.M. = \frac{N}{\sum f / x} = \frac{44}{1.1692} = 37.63$

ii)

$$\operatorname{Log} (\mathrm{GM}) = \frac{\sum f x_{i}}{N} = \frac{69.59623}{44} = 1.5817325$$

The geometric mean is $\mathrm{GM} = 10^{1.5817325} = 38.17$

iii) To find the mode of grouped distribution, the following formula will be used:

$$Mode = l + \frac{f_{1} - f_{0}}{2f_{1} - f_{0} - f_{2}} \cdot h,$$

where $l$ is the lower limit of model class, $f_{0}$ is the frequency of class preceding, $f_{1}$ is the frequency of that class and $f_{2}$ is the frequency of class succeeding the model class respectively, $h$ is the class width.

The mode containing class is [35-39] has the biggest frequency 13.

So the mode value is

$$Mode = 35 + \frac{13 - 9}{2 \cdot 13 - 9 - 10} \cdot 4 = 37\frac{2}{7} \approx 16.29.$$

Answer: i) 37.63; ii) 38.17; iii) 16.29.

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