Understanding the Health Club Membership Data

The problem provides data about the distribution of members (male and female) and male members across five different health clubs, labeled A through E. We are given the percentage distribution for both total members and male members across these clubs, along with two specific absolute numbers: the total members in health club C and the number of male members in health club E. Our goal is to find the median number of male members among all five clubs.

Extracting and Calculating Absolute Numbers

We are given the following key pieces of information:

• Total members in health club C = 1764.
• Percentage of total members in club C = 14%.

Let the total number of members across all five clubs be \(T\). We can write the equation:

\(14\%\) of \(T = 1764\)

\(0.14 \times T = 1764\)

\(T = \frac{1764}{0.14} = 12600\)

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

We are also given:

• Number of male members in health club E = 576.
• Percentage of total male members in club E = 8%.

Let the total number of male members across all five clubs be \(M\). We can write the equation:

\(8\%\) of \(M = 576\)

\(0.08 \times M = 576\)

\(M = \frac{576}{0.08} = 7200\)

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

Calculating Male Members in Each Health Club

Now that we know the total number of male members (\(M = 7200\)), we can use the percentage distribution of male members for each club to find the absolute number of male members in each club.

• Health Club A: \(21\%\) of \(7200 = 0.21 \times 7200 = 1512\) male members.
• Health Club B: \(32\%\) of \(7200 = 0.32 \times 7200 = 2304\) male members.
• Health Club C: \(19\%\) of \(7200 = 0.19 \times 7200 = 1368\) male members.
• Health Club D: \(20\%\) of \(7200 = 0.20 \times 7200 = 1440\) male members.
• Health Club E: \(8\%\) of \(7200 = 0.08 \times 7200 = 576\) male members. (This matches the given information, confirming our total male members calculation is correct).

The number of male members in the five health clubs A, B, C, D, and E are 1512, 2304, 1368, 1440, and 576 respectively.

Finding the Median Number of Male Members

The median is the middle value in a dataset when the values are arranged in order. We have the following numbers of male members for the five health clubs:

1512, 2304, 1368, 1440, 576

First, we need to arrange these numbers in ascending order:

576, 1368, 1440, 1512, 2304

Since there are 5 numbers (an odd number), the median is the middle value, which is the 3rd number in the sorted list.

The sorted list is: 576, 1368, 1440, 1512, 2304.

The third value is 1440.

Therefore, the median number of male members for all five health clubs is 1440.

Sorted list of male members: 576, 1368, 1440, 1512, 2304

Median = 1440

Revision Table: Key Calculations

Additional Information: Understanding Median

The median is a measure of central tendency. It is the middle value in a dataset that has been ordered from least to greatest. Unlike the mean (average), the median is not affected by extremely large or small values (outliers).

• If the dataset has an odd number of values, the median is the single middle value.
• If the dataset has an even number of values, the median is typically the average of the two middle values.

In this problem, we had 5 health clubs, resulting in 5 distinct values for male members. Since 5 is an odd number, the median is simply the 3rd value after sorting the list.

Data interpretation questions often require calculating various statistical measures like mean, median, mode, range, ratios, and percentages based on given data tables or charts. Understanding how to calculate these measures correctly is crucial.