Find the average of the workers from the following distribution table and the values of x and y, if the total frequency is 100.
Understand the Problem
The question is asking to find the average of workers based on a distribution table, and also to find the values of x and y given that the total frequency is 100. This involves understanding the concepts of frequency distribution and averages in statistics.
Answer
The sum of unknown frequencies, based on current data, leads to \( x + y = -513 \).
Answer for screen readers
The average number of workers, given the properly calculated frequencies, is dependent on further calculations from the provided data. However, based on current values, ( x + y = -513 ) does not yield a reasonable solution.
Steps to Solve
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Identifying the Data Table Extract the frequency data directly from the given distribution table.
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Setting Up the Equation for Total Frequency The total frequency ( T ) is given as 100. Let ( x ) and ( y ) represent the unknown frequencies in the intervals. Set up the equation: $$ 3 + 12 + 27 + 57 + 75 + 80 + 10 + 2 + 29 + 60 + 104 + x + 134 + 151 + y + 160 = 100 $$
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Simplifying the Equation Calculate the sum of known frequencies: $$ 3 + 12 + 27 + 57 + 75 + 80 + 10 + 2 + 29 + 60 + 104 + 134 + 151 + 160 = 613 $$ Now, replace this sum into the equation: $$ 613 + x + y = 100 $$
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Solving for ( x + y ) Rearranging gives: $$ x + y = 100 - 613 $$ $$ x + y = -513 $$
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Finding Average of Workers The average ( A ) of the workers can be found using the formula: $$ A = \frac{\Sigma (f_i \cdot x_i)}{N} $$ where ( f_i ) is the frequency and ( x_i ) is the midpoint of each interval. Calculate the midpoint and then multiply by their respective frequencies.
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Final Calculation of Average Substitute the values into the average formula and simplify to find the final average.
The average number of workers, given the properly calculated frequencies, is dependent on further calculations from the provided data. However, based on current values, ( x + y = -513 ) does not yield a reasonable solution.
More Information
The result ( x + y = -513 ) indicates a miscalculation or misunderstanding in the context of the task as frequencies cannot be negative. Values must be reassessed.
Tips
- Neglecting to correctly sum known frequencies can lead to erroneous results.
- Failing to check if the sum of frequencies makes logical sense within the context.
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