Understanding the Night Shift Worker Data

The question provides a table showing the percentage distribution of people working the night shift across six different industries and the percentage of females within the night shift workers for each industry. We are given the total number of people working the night shift in the city is 80500. Our goal is to find the total number of males working in the night shift across all these industries.

To find the total number of males, we first need to determine the number of night shift workers in each industry, then calculate the number of females in the night shift for each industry, and finally subtract the number of females from the total workers in each industry to get the number of males. Summing up the males from all industries will give us the total.

Calculating Total Night Shift Workers per Industry

The total number of people working in the night shift is 80500. We can calculate the number of workers in each industry by using the given percentage distribution:

• IT: $\text{Total workers} = 80500 \times \frac{12}{100} = 805 \times 12 = 9660$
• Sports: $\text{Total workers} = 80500 \times \frac{18}{100} = 805 \times 18 = 14490$
• Call centre: $\text{Total workers} = 80500 \times \frac{32}{100} = 805 \times 32 = 25760$
• Sales: $\text{Total workers} = 80500 \times \frac{8}{100} = 805 \times 8 = 6440$
• Banking: $\text{Total workers} = 80500 \times \frac{14}{100} = 805 \times 14 = 11270$
• Chemicals: $\text{Total workers} = 80500 \times \frac{16}{100} = 805 \times 16 = 12880$

Calculating Number of Females in Night Shift per Industry

Now, we calculate the number of females in the night shift for each industry using the total workers in that industry and the percentage of females:

• IT: $\text{Number of females} = 9660 \times \frac{20}{100} = 966 \times 2 = 1932$
• Sports: $\text{Number of females} = 14490 \times \frac{20}{100} = 1449 \times 2 = 2898$
• Call centre: $\text{Number of females} = 25760 \times \frac{45}{100} = 257.6 \times 45 = 11592$
• Sales: $\text{Number of females} = 6440 \times \frac{60}{100} = 644 \times 6 = 3864$
• Banking: $\text{Number of females} = 11270 \times \frac{40}{100} = 1127 \times 4 = 4508$
• Chemicals: $\text{Number of females} = 12880 \times \frac{15}{100} = 128.8 \times 15 = 1932$

Calculating Number of Males in Night Shift per Industry

The number of males in each industry's night shift is the total number of workers minus the number of females:

• IT: $\text{Number of males} = 9660 - 1932 = 7728$
• Sports: $\text{Number of males} = 14490 - 2898 = 11592$
• Call centre: $\text{Number of males} = 25760 - 11592 = 14168$
• Sales: $\text{Number of males} = 6440 - 3864 = 2576$
• Banking: $\text{Number of males} = 11270 - 4508 = 6762$
• Chemicals: $\text{Number of males} = 12880 - 1932 = 10948$

Calculating Total Number of Males Across All Industries

To find the total number of males working in the night shift from all industries together, we sum the number of males calculated for each industry:

Total Males = (Males in IT) + (Males in Sports) + (Males in Call centre) + (Males in Sales) + (Males in Banking) + (Males in Chemicals)

Total Males = $7728 + 11592 + 14168 + 2576 + 6762 + 10948$

Total Males = $19320 + 14168 + 2576 + 6762 + 10948$

Total Males = $33488 + 2576 + 6762 + 10948$

Total Males = $36064 + 6762 + 10948$

Total Males = $42826 + 10948$

Total Males = $53774$

Thus, the total number of males working in the night shift from all the industries together is 53774.

Revision Table: Night Shift Calculations

Additional Information on Percentage Distribution Problems

Percentage distribution problems, often found in data interpretation questions, require careful calculation based on given percentages and total values. Here are some key concepts:

• Understanding Percentage: A percentage represents a part per hundred. To convert a percentage to a decimal, divide by 100 (e.g., $12\% = 12/100 = 0.12$).
• Calculating Part from Whole: If you know the total (whole) and the percentage of a part, the value of the part is calculated as: $\text{Part} = \text{Whole} \times \frac{\text{Percentage}}{100}$.
• Calculating Percentage of a Subset: The percentage of females in this problem is calculated based on the number of night shift workers within that specific industry, not the total night shift workers across all industries. It's crucial to identify the correct base for the percentage calculation.
• Finding the Complement: If you know the percentage or number of one category (like females), you can find the other category (like males) by subtracting from the total for that group: $\text{Number of Males} = \text{Total in Group} - \text{Number of Females}$. Similarly, $\text{Percentage of Males} = 100\% - \text{Percentage of Females}$.
• Summing up Totals: When asked for a total across different categories (like the total number of males from all industries), you must sum the individual values calculated for each category.

These steps and concepts are fundamental to solving data interpretation questions involving percentages and distributions across different groups or categories.