Math Problem Statement

A local company carried out their annual employee survey. While waiting for the main results to be analysed, it received details of the numbers of people who completed the survey for each business area.

The table below shows survey response rates by business area and the number of employees asked to complete the survey.

Business Area Number of responses Total surveyed Response rate Finance 10 20 50% Human Resources 13 30 43% Information Technology 18 64 28% Policy 118 380 31% Customer Services 132 365 36% Operations 216 590 37% Facilities 18 52 35% Commercial 33 51 65% Overseas 28 67 42%

What is the total percentage of responses received?

Solution

To calculate the total percentage of responses received across all business areas, we need to first determine the overall response rate. This involves:

  1. Summing the total number of responses.
  2. Summing the total number of employees surveyed.
  3. Dividing the total number of responses by the total number of employees surveyed, and then multiplying by 100 to get the percentage.

Let's break it down step by step.

Step 1: Summing the total number of responses

10+13+18+118+132+216+18+33+28=58610 + 13 + 18 + 118 + 132 + 216 + 18 + 33 + 28 = 586

Step 2: Summing the total number of employees surveyed

20+30+64+380+365+590+52+51+67=161920 + 30 + 64 + 380 + 365 + 590 + 52 + 51 + 67 = 1619

Step 3: Calculating the total response rate

Total response rate=(5861619)×100\text{Total response rate} = \left( \frac{586}{1619} \right) \times 100

Total response rate36.19%\text{Total response rate} \approx 36.19\%

So, the overall percentage of responses received is approximately 36.19%.

Would you like any further details or clarifications on this?

Here are 5 follow-up questions to expand this discussion:

  1. How can individual department response rates impact overall company morale?
  2. What could be done to improve response rates across departments with lower participation?
  3. How does the response rate relate to the validity or reliability of the survey data?
  4. What strategies could the company employ to encourage more survey completions in the future?
  5. What could be the consequences of low response rates in critical departments like Human Resources?

Tip: When calculating totals or averages, always double-check that all components (like responses and surveyed) are included in your calculations for accuracy.

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Math Problem Analysis

Mathematical Concepts

Percentage
Proportion
Summation

Formulas

Total Response Rate = (Total Number of Responses / Total Number of Employees Surveyed) × 100

Theorems

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Suitable Grade Level

Grades 5-7