To answer the question about the inference we can make from analyzing the data in the given table, we need to look closely at the measures of center (mean, median, mode) and measures of variation (range, Mean Absolute Deviation).
Let's break down each option one by one:
1. There is more variation in the science scores.
- Both range and Mean Absolute Deviation (MAD) indicate variation in the data.
- From the table, the range for science is 40, while the range for math is 15.
- The MAD for science is 14.4, which is significantly higher compared to the MAD for math which is 4.0.
- Therefore, it is clear that there is more variation in the science scores.
2. Tyrell prefers math over science.
- This inference is not supported by the data shown in the table. The table only gives the measures of center and variation, not any indication of Tyrell's preferences.
3. The mode is the best measure of the typical score for both science and math.
- The data does not specifically indicate whether the mode is the best measure for the typical score. Typically, the "best" measure of the central tendency should be determined considering the spread and shape of the distribution, and this cannot be conclusively determined from only the given values.
- For instance, the mode for science is 60, and for math it is 85. Without more context or data distribution, we cannot conclude that mode is the best measure.
4. The median for each subject is the same as the mean.
- For science: Median is 80 and Mean is 78.
- For math: Both Median and Mean are 80.
- This statement is partially true since it applies correctly only to math scores, not to science scores.
Given these considerations, the most accurate and supported inference from analyzing the data in the table is the first option:
There is more variation in the science scores.
