Answer: To approximate the mean of the grouped data, we can use the midpoint of each class interval and the frequency of each interval. The formula for the mean of grouped data is:
Mean = (Σ(midpoint × frequency)) / (Σfrequency)
Let's calculate the mean for the given grouped data:
Class Interval: 1-2, 3-4, 5-6, 7-8, 9-10
Frequency: 135, 29, 12, 18, 2
To find the midpoint of each class interval, we take the average of the lower and upper bounds. The midpoints are: 1.5, 3.5, 5.5, 7.5, 9.5.
Now, let's calculate the mean:
Mean = ((1.5 × 135) + (3.5 × 29) + (5.5 × 12) + (7.5 × 18) + (9.5 × 2)) / (135 + 29 + 12 + 18 + 2)
Mean = (202.5 + 101.5 + 66 + 135 + 19) / 196
Mean ≈ 525 / 196
Mean ≈ 2.67
Therefore, the approximate mean of the grouped data is 2.67.
For the second question about the trimmed mean, we are given the scores 61, 66, 68, 82, 84, 86, 88, 90, 92, and 93. To find the 10% trimmed mean, we remove the lowest and highest 10% of the data.
10% of the data is 10% * 10 = 1. We remove the lowest and highest score, which are 61 and 93.
Remaining scores: 66, 68, 82, 84, 86, 88, 90, 92.
Now, we calculate the mean of these remaining scores:
Mean = (66 + 68 + 82 + 84 + 86 + 88 + 90 + 92) / 8
Mean = 656 / 8
Mean = 82
Therefore, the 10% trimmed mean of the given data is 82.
For the third question about finding the range of a data set represented in a stem-and-leaf plot, we need to identify the smallest and largest values in the data set.
Without the stem-and-leaf plot, it is not possible to accurately determine the range of the data set. The stem-and-leaf plot provides a visual representation of the data, but without the actual values, we cannot determine the range.
Explanation: