Data Interpretation Solution: Average Female Members in Health Clubs

This problem requires us to calculate the average number of female members across three specific health clubs (A, B, and C) based on the provided table showing the percentage distribution of total members and male members.

Understanding the Given Data

We are given a table with percentage distributions for five health clubs (A, B, C, D, E) in the year 2022:

• Percentage of total members (male + female) in each club relative to the total members across all clubs.
• Percentage of male members in each club relative to the total male members across all clubs.

We are also given two absolute values:

• Total number of members (both male and female) in health club C is 1764.
• Number of male members in health club E is 576.

Step-by-Step Calculation

Step 1: Calculate Total Number of Members Across All Health Clubs

We know that 14% of the total number of members is equal to 1764 (the number of members in health club C).

Let \(T\) be the total number of members across all five clubs.

\(14\% \text{ of } T = 1764\)

\(\frac{14}{100} \times T = 1764\)

\(T = \frac{1764 \times 100}{14}\)

\(T = 126 \times 100\)

\(T = 12600\)

So, the total number of members across all health clubs is 12600.

Step 2: Calculate Total Number of Male Members Across All Health Clubs

We know that 8% of the total number of male members is equal to 576 (the number of male members in health club E).

Let \(M\) be the total number of male members across all five clubs.

\(8\% \text{ of } M = 576\)

\(\frac{8}{100} \times M = 576\)

\(M = \frac{576 \times 100}{8}\)

\(M = 72 \times 100\)

\(M = 7200\)

So, the total number of male members across all health clubs is 7200.

Step 3: Calculate Total Members and Male Members for Health Clubs A, B, and C

Using the total numbers calculated above and the percentages from the table:

• Health Club A:
  • Total members in A = 21% of 12600 = \(\frac{21}{100} \times 12600 = 21 \times 126 = 2646\)
  • Male members in A = 21% of 7200 = \(\frac{21}{100} \times 7200 = 21 \times 72 = 1512\)
• Health Club B:
  • Total members in B = 33% of 12600 = \(\frac{33}{100} \times 12600 = 33 \times 126 = 4158\)
  • Male members in B = 32% of 7200 = \(\frac{32}{100} \times 7200 = 32 \times 72 = 2304\)
• Health Club C:
  • Total members in C = 14% of 12600 = \(\frac{14}{100} \times 12600 = 14 \times 126 = 1764\) (Matches given data)
  • Male members in C = 19% of 7200 = \(\frac{19}{100} \times 7200 = 19 \times 72 = 1368\)

Step 4: Calculate Female Members for Health Clubs A, B, and C

Number of female members = Total members - Number of male members

• Female members in A = Total members in A - Male members in A = \(2646 - 1512 = 1134\)
• Female members in B = Total members in B - Male members in B = \(4158 - 2304 = 1854\)
• Female members in C = Total members in C - Male members in C = \(1764 - 1368 = 396\)

Step 5: Calculate the Average Number of Female Members in Health Clubs A, B, and C

Average = Sum of female members / Number of health clubs

Sum of female members in A, B, C = Female members in A + Female members in B + Female members in C

Sum = \(1134 + 1854 + 396 = 3384\)

Average = \(\frac{3384}{3}\)

Average = \(1128\)

Thus, the average number of female members in health clubs A, B, and C is 1128.

Summary Table

Average Female Members (A, B, C) = \(\frac{1134 + 1854 + 396}{3} = \frac{3384}{3} = 1128\).

Revision Table: Key Concepts

Additional Information: Data Interpretation Tips

Data interpretation questions often involve analyzing tables, charts, or graphs to extract relevant information and perform calculations. Here are some tips:

• Read the question carefully to understand exactly what is being asked.
• Scan the entire table or chart to get a general overview of the data.
• Identify the units used (e.g., absolute numbers, percentages, ratios).
• Note any total values or specific data points provided outside the main table/chart, as these are often crucial for calculations.
• Break down complex calculations into smaller, manageable steps.
• Be careful with percentage calculations, ensuring you are using the correct base value (e.g., percentage of total members vs. percentage of male members).
• Use quick calculation methods or approximations where appropriate, but maintain accuracy for final answers.
• Double-check your calculations, especially when dealing with multiple steps.
• Practice with various types of data representation (tables, bar graphs, pie charts, line graphs) to improve your skills.

This question combined percentage calculations with finding missing totals to arrive at the required average. It's a typical example of data interpretation problems asked in competitive exams.