7. Which central tendency is most appropriate for the following set of data? (hint: these are scores on a quiz) X: 11, 12, 14, 15, 16, 16, 16, 17, 17, 19
a. Mode
b. You can’t tell due to the skewedness
c. Median
d. Mean
Find the 25th percentile for the data in problem 7.
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c. Median
To find the median of the data set, we first need to arrange the scores in ascending order:
11, 12, 14, 15, 16, 16, 16, 17, 17, 19
Since there are an even number of scores (10 total), the median is the average of the two middle numbers. In this case, the middle numbers are the 5th and 6th numbers (16 and 16).
Therefore, the median is:
(16 + 16) / 2 = 16
So, the median score for this data set is 16.
To find the 25th percentile, we need to determine which score is at the 25th percentile. There are 10 total scores, so the 25th percentile would be at the 2.5th position (25% of 10 = 2.5).
The 2.5th position falls between the 2nd and 3rd scores, which are 12 and 14.
To find the exact value at the 25th percentile, we can use linear interpolation:
25th percentile = 12 + (14 - 12) * 0.5 = 13
Therefore, the 25th percentile for the data in problem 7 is 13.
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