The median would be a better measure for the center of the data for of which of the following data sets?a. {9, 11, 14, 16, 1, 12, 15, 17}b. {0.9, 1.2, 2.2, 1.6, 2.1, 3}c. {4, 6, 5, 8, 3, 4, 7, 5}d. {6, 6, 6, 7, 7, 8, 8, 8, 8, 9}
To determine which data set would be better suited for the median as a measure of central tendency, let’s calculate the median for each set and analyze the results:
a
To determine which data set would be better suited for the median as a measure of central tendency, let’s calculate the median for each set and analyze the results:
a. {9, 11, 14, 16, 1, 12, 15, 17}
To find the median, we first arrange the data in increasing order: {1, 9, 11, 12, 14, 15, 16, 17}. Then, as the set contains 8 data points, the median would be the average of the two middlemost values, which in this case are 12 and 14. Therefore, the median is (12 + 14) / 2 = 26 / 2 = 13.
b. {0.9, 1.2, 2.2, 1.6, 2.1, 3}
Sorting this set gives us {0.9, 1.2, 1.6, 2.1, 2.2, 3}. Since the set contains an odd number of data points, the median is simply the middlemost value, which is 1.6.
c. {4, 6, 5, 8, 3, 4, 7, 5}
Arranging the data in increasing order, we have {3, 4, 4, 5, 5, 6, 7, 8}. This set also contains an even number of data points, so the median will be the average of the two middlemost values, which in this case are 5 and 5. Therefore, the median is (5 + 5) / 2 = 10 / 2 = 5.
d. {6, 6, 6, 7, 7, 8, 8, 8, 8, 9}
Sorting this set gives us {6, 6, 6, 7, 7, 8, 8, 8, 8, 9}. As the set contains 10 data points, the median will again be the average of the two middlemost values, which are 7 and 8. Therefore, the median is (7 + 8) / 2 = 15 / 2 = 7.5.
Now, let’s analyze the results:
a. The median for this data set is 13.
b. The median for this data set is 1.6.
c. The median for this data set is 5.
d. The median for this data set is 7.5.
Since the median is most appropriate for representing the center of a data set with a symmetrical distribution, we look for data sets where the median aligns with the anticipated center. In this case, sets b and d have medians that align well with the centers of their distributions. Therefore, the answer is b and d.
In summary, for the given data sets, the median would be a better measure for the center of the data for options b and d.
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