On their first five history assignments, Evan received the following scores 1) Identify the measures of center (mean, median, mode) mean: 88.8 median: 91 mode: 2) Identify the IQR. 3) Interpret the IQR: Little variability or big variability?

To analyze Evan's scores and answer your questions, we first need to establish the scores he received on his five history assignments. Since you provided the mean, median, and asked for the mode and IQR, let's assume the scores are as follows: 1. **Scores**: Let's assume Evan's scores are: 85, 88, 91, 92, 95. ### 1) Measures of Center - **Mean**: Given as 88.8 (but based on the assumed scores, the mean would actually be calculated as follows): \[ \text{Mean} = \frac{85 + 88 + 91 + 92 + 95}{5} = \frac{451}{5} = 90.2 \] (This indicates that the assumed scores may not be accurate for the given mean of 88.8. We can adjust the scores accordingly if needed.) - **Median**: The median is the middle score when the scores are arranged in order. For the assumed scores (85, 88, 91, 92, 95), the median is 91. - **Mode**: The mode is the score that appears most frequently. In the assumed scores, there is no repeating score, so there is no mode. If we had scores like 85, 88, 91, 91, 95, then the mode would be 91. ### 2) Identify the IQR To find the Interquartile Range (IQR), we need to find the first quartile (Q1) and the third quartile (Q3). - **Ordered Scores**: 85, 88, 91, 92, 95 - **Q1**: The median of the first half (85, 88) is (85 + 88) / 2 = 86.5. - **Q3**: The median of the second half (91, 92, 95) is 92. - **IQR**: \[ \text{IQR} = Q3 - Q1 = 92 - 86.5 = 5.5 \] ### 3) Interpret the IQR The IQR of 5.5 indicates the range within which the middle 50% of the scores fall. - **Interpretation**: A smaller IQR suggests that the scores are relatively close to each other, indicating little variability. Conversely, a larger IQR would suggest more spread out scores, indicating greater variability. In this case, an IQR of 5.5 suggests **little variability** in Evan's scores. ### Summary - **Mean**: 88.8 (or 90.2 based on assumed scores) - **Median**: 91 - **Mode**: None (or 91 if adjusted scores) - **IQR**: 5.5 - **Interpretation**: Little variability in scores. If you have specific scores for Evan, please provide them, and I can adjust the calculations accordingly!