Answer

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**Hint:**In order to solve this problem, we need to understand the meaning of the weighted average. The weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. Also, we must know the formula for the mean of n number of terms. The formula is given by $\text{Mean = }\dfrac{\text{Total weight}}{\text{Total number of people}}$ .

**Complete step-by-step solution:**We are given the data of the weight of 60 workers in a factory.

We can see that 5 people have a weight of 60 kgs.

8 people have a weight of 61kgs.

14 people have a weight of 62 kgs.

16 people have a weight of 63 kgs.

10 people have a weight of 64 kgs.

7 people have a weight of 65 kgs.

Hence, we need to add the weight of 60 kgs 5 times as we have 5 people of the same weight.

Hence, we can do the same process for all the categories.

Adding another row and multiplying the weight of each person to the number of persons in that category, we get,

Weight (in kg) | 60 | 61 | 62 | 63 | 64 | 65 |

Number of workers | 5 | 8 | 14 | 16 | 10 | 7 |

The total weight (in kg) | 60 x 5 = 300 | 61 x 8 = 488 | 62 x 14 = 868 | 63 x 16 = 1008 | 64 x 10 = 640 | 65 x 7 = 455 |

Now, we have the sum of all the weights in each category,

We need to add the weight in all the categories to get the sum of all the 60 people.

Adding all the weight we get,

Total weight = 300 + 488 + 868 + 1008 + 640 + 455 = 3759.

Now, we need the formula for the mean for n number of people.

The formula is given as follows,

$\text{Mean = }\dfrac{\text{Total weight}}{\text{Total number of people}}$

Substituting all the values we get,

$\text{Mean = }\dfrac{3759}{60}$

Solving this we get,

$\text{Mean = 62}\text{.65}$ kg.

**Therefore, the mean weight of a worker is 62.65 kgs.**

**Note:**In this problem, we need to understand that each category has a certain weightage. The column of weighing 60 kg has the least weightage because it contains the lowest number of people, whereas people with 16 people has the highest weightage. We can also cross-check that as it is the mean the answer will lie between 60 and 65.

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