Two companies surveyed employee satisfaction scores (1-10 scale). Company X: mean = 6.8, MAD = 1.4, range = 7. Company Y: mean = 7.2, MAD = 2.1, range = 8. An HR consultant needs to identify which company has more satisfied employees and which has more consensus. What should the consultant conclude?
- Company Y has more satisfied employees and more consensus among employees based on the statistical measures provided.
- Company X has more satisfied employees and more consensus among employees based on the statistical measures provided.
- Company X has more satisfied employees, but Company Y has more consensus among employees based on the measures.
- Company Y has more satisfied employees, but Company X has more consensus among employees based on the measures. (correct answer)
Explanation: When analyzing employee satisfaction data, you need to understand what different statistical measures tell you. The mean shows average satisfaction level, while measures of spread like MAD (Mean Absolute Deviation) and range indicate how much agreement or consensus exists among employees. To determine satisfaction levels, compare the means directly. Company Y's mean of 7.2 is higher than Company X's mean of 6.8, so Company Y has more satisfied employees on average. For consensus, look at the spread measures - smaller values indicate more agreement. Company X has a MAD of 1.4 compared to Company Y's 2.1, and Company X's range is 7 versus Company Y's 8. Both measures show Company X has less variability, meaning employees' scores cluster more tightly around the average. This indicates greater consensus at Company X. Looking at the answer choices: Choice A incorrectly claims Company Y has more consensus, when their higher MAD and range actually show less consensus. Choice B gets both comparisons wrong - it claims Company X has higher satisfaction when their mean is actually lower. Choice C reverses the satisfaction comparison, incorrectly stating Company X has more satisfied employees when Company Y's mean is higher. Choice D correctly identifies that Company Y has higher satisfaction (higher mean) while Company X has more consensus (lower MAD and range). Remember: mean indicates the "what" (level of satisfaction), while measures of spread like MAD and range indicate the "how much agreement" (consensus). Always match the right statistic to what you're trying to measure.