To find the mean of the students' scores from the given table, we’ll use the concept of a grouped frequency distribution. Here are the steps:

1. Identify the Midpoint (Class Mark) for Each Score Range: The midpoint for each range is calculated by averaging the lower and upper limits.
2. Multiply Each Midpoint by its Frequency to get the total for each range.
3. Sum of the Products: Add up all the products obtained from step 2.
4. Sum of Frequencies: Add up all the frequencies.
5. Calculate the Mean using the formula:

$\text{Mean} = \frac{\sum ( \text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}}$

Calculations

Summing Up

• Sum of $f \times x$: $234 + 292 + 544 + 630 + 696 + 318 = 2714$
• Sum of Frequencies ($f$): $3 + 4 + 8 + 10 + 12 + 6 = 43$

Mean Calculation

$\text{Mean} = \frac{2714}{43} \approx 63.14$

The mean score of the students is approximately 63.14.

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Related Questions

1. How would you calculate the median score from this grouped data?
2. What does the mean score tell us about the students' performance?
3. How can we calculate the mode for grouped data like this?
4. What is the significance of choosing the midpoint for each range in finding the mean?
5. How would the mean change if the frequencies for the score ranges were altered?

Tip

In grouped frequency distributions, the midpoint approximation gives a close estimate of the central tendency but may not be exact since individual scores within the ranges are not known.