Subjects statistics

Iqr Standard Deviation 9C2021

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1. **State the problem:** We want to find the Interquartile Range (IQR) and the Standard Deviation of the differences in MPG (highway - city) for 21 midsize cars from model year 2020. 2. **Understanding IQR:** The IQR is the range of the middle 50% of the data. It is calculated as $$\text{IQR} = Q_3 - Q_1$$ where $Q_1$ is the first quartile (25th percentile) and $Q_3$ is the third quartile (75th percentile). 3. **Understanding Standard Deviation:** The standard deviation measures how spread out the data is around the mean. It is calculated as $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $x_i$ are the data points, $\bar{x}$ is the mean, and $n$ is the number of data points. 4. **Using the dot plot:** The dot plot shows differences mostly between 6 and 11, with a dense cluster around 9 and 10. To find exact IQR and standard deviation, we need the raw data or summary statistics (quartiles and mean). 5. **Conclusion:** Without the exact data values or summary statistics, we cannot compute precise IQR or standard deviation. However, the IQR is the difference between the 75th and 25th percentile differences, and the standard deviation quantifies typical variation from the mean difference. If you provide the data or quartile values, I can calculate these exactly.