Final answer:
The true statement about the mean of the sums from the frequency table is that the mean is the same as the median. After calculating, we find that both the mean and the median are 11.
Step-by-step explanation:
The question involves determining the true statement about the mean of the sums of two spinners, given the frequency table. To find the mean of a frequency table, we multiply each sum by its frequency, add those products together, and then divide by the total number of observations. The sums provided are 5, 7, 9, 11, 13, 15, and 17, with respective frequencies of 1, 2, 3, 4, 3, 2, and 1.
Calculating the weighted sum:
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- (5 × 1) + (7 × 2) + (9 × 3) + (11 × 4) + (13 × 3) + (15 × 2) + (17 × 1)
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- = 5 + 14 + 27 + 44 + 39 + 30 + 17
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- = 176
Thus, none of the statements about the mean provided in the question are correct; the actual mean is 11. When considering the range of values provided (from 5 to 17), the mean is not the same as the range (which is 12). The median, which is the middle value when the sums are listed in order, is 11 since it is the fourth value of seven equally spaced data points in this case. Since the median also equals 11 and matches the mean we calculated, the statement "The mean is the same as the median" is the correct assertion about the characteristics of the data.