Question

The mean height of $25$ male workers in a factory is $61$ cm and the mean height of $35$ female workers in the same factory is $58$ cm. The combined mean height of $60$ workers in the factory is
A) $59.25$
B) $59.5$
C) $59.75$
D) $58.75$

Answer 1

Here it is given that, mean height of male workers and mean height of the female workers. We have to find the combined mean height of them. At first, we will find the total height of male workers. Then, we will find the total height of female workers. Then, we will find the total height of male and female workers. Finally we can find the mean height of the total workers.

Complete step-by-step solution:
The given data are: the mean height of $25$ male workers in a factory is $61$ cm and the mean height of $35$ female workers in the same factory is $58$ cm. There are total $60$ workers in the factory.
We have to find the combined mean height of $60$ workers in the factory.
We know that the mean height of male workers is $61$ cm.
The number of male workers is $25$.
The total height of the male workers $= 25 \times 61$ cm
Simplifying we get,
The total height of the male workers $= 1525$ cm
The mean height of female workers is $58$ cm.
The number of male workers is $35$.
The total height of the female workers $= 35 \times 58$ cm
Simplifying we get,
The total height of the female workers $= 2030$ cm
Number of total workers $= 25 + 35 = 60$
Total height of $60$ workers $= 2030 + 1525$ cm
Simplifying we get,
Total height of $60$ workers $= 3555$ cm
So, the mean height of the $60$ workers $= 3555 \div 60$ cm
Simplifying we get,
The mean height of the $60$ workers $= 59.25$ cm
Hence, the combined mean height of $60$ workers in the factory is $59.25$ cm.

$\therefore$ The correct option is A.

Note: Mean (or average) of observations, as we know, is the sum of the values of all the observations divided by the total number of observations.
Let us consider, $n$ numbers of terms such as: ${x_1},{x_2},...,{x_n}.$
So, the mean of the terms is $= \dfrac{{{x_1} + {x_2} + {x_3} + ... + {x_n}}}{n}$
Combined mean: A combined mean is simply a weighted mean, where the weights are the size of each group. For more than two groups:
Add the means of each group each weighted by the number of individuals or data points.
Divide the sum from the first step by the sum total of all individuals (or data points).