Final Answer:
The comparison between the difference of the means and the Mean Absolute Deviation (MAD) is 3.5 (c), rounded to the nearest tenth.
Step-by-step explanation:
To compare the difference of the means and the MAD, we first find the mean of the collected data at the beginning and end of the year. Then, we calculate the MAD. Suppose the mean time spent on the math puzzle at the beginning of the year is μ₁ and at the end of the year is μ₂.
Next, we determine the difference between the means (μ₂ - μ₁). Then, to find the MAD, we calculate the average absolute difference between each data point and the mean. The formula for MAD involves finding the absolute differences, summing them, and dividing by the number of data points.
After computing both values, we compare the difference of the means to the MAD. If the difference of the means is close to the MAD, it suggests that the variation within the data points is comparatively low, indicating a more consistent distribution of values.
For instance, if the difference of the means turns out to be 3.5 and the MAD is also 3.5, this suggests that, on average, the individual data points are approximately 3.5 units away from the mean. Therefore, the closeness in these values indicates a consistent spread of data around the mean, resulting in the comparison value of 3.5.
Question:
When comparing the difference of the means and the Mean Absolute Deviation (MAD) calculated from the data Quentin collected on the time students spent completing a math puzzle at the beginning and end of the year, the resulting comparison value is 3.5 (C), rounded to the nearest tenth. What does this comparison suggest about the variability and consistency of the data sets?