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Mean Median Mode 75Efaf

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Mean Median Mode 75Efaf


1. **Problem Statement:** Given the total time spent studying by 30 Grade 9 students, arranged in class intervals with frequencies, mid-points, and cumulative frequencies, we are to compute the mean, median, and mode of the data. 2. **Mean Calculation:** The mean is calculated using the formula: $$\overline{X} = \frac{\sum fX_m}{n}$$ where $f$ is the frequency, $X_m$ is the mid-point of each class interval, and $n$ is the total number of observations. 3. **Applying the formula:** Given $\sum fX_m = 295$ and $n = 30$, we have: $$\overline{X} = \frac{295}{30} = 9.83$$ This means the average study time is approximately 9.83 hours. 4. **Median Calculation:** The median class is identified as the class where the cumulative frequency just exceeds $\frac{n}{2} = 15$. Here, it is the class 1-10. The median formula is: $$\tilde{X} = X_{LB} + \left(\frac{\frac{n}{2} -