If one student submits 25 additional…

Mathematics Questions

If one student submits 25 additional drawings, will the mean absolute deviation (MAD) of the art class’s drawing submissions increase, regardless of whether the drawings belong to Amy or Emily?

Short Answer

The Mean Absolute Deviation (MAD) currently stands at 10, indicating a certain level of data variability. Adding drawings from Amy will decrease the MAD due to lower variability in her contributions, while drawings from Emily will increase the MAD because of their higher variability.

Step-by-Step Solution

Step 1: Understand the Current MAD

The Mean Absolute Deviation (MAD) is a measure of how spread out the values in a data set are from the average. In this case, the current MAD of the data in the table is 10, which indicates a certain level of variability. It’s important to focus on the values and how they are distributed around the mean to comprehend how additional drawings will affect the MAD.

Step 2: Analyze Amy’s Drawings Impact

If the additional drawings come from Amy, it is stated that the MAD of the dataset will decrease. This suggests that Amy’s contributions likely have less variability compared to the existing data, thereby pulling the overall spread closer to the mean. The addition of less diverse data points reduces the average distance of all data points from the mean, ultimately leading to a lower MAD.

Step 3: Analyze Emily’s Drawings Impact

In contrast, if the additional drawings are from Emily, the MAD of the dataset will increase. This indicates that Emily’s contributions may possess higher variability,

Related Concepts

Mean absolute deviation

Mad is a statistical measure that quantifies the average distance of each data point from the mean of a dataset, indicating the spread or variability of the data.

Data variability

Variability refers to how much the data points in a dataset differ from each other, influencing indicators like the mad when new data points are added.

Effective data addition

Effective data addition refers to the impact that including new data points can have on the overall dataset’s statistical measures, such as the mad, either increasing or decreasing it based on the nature of the new data.

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