In the following set, which measure of central tendency would probably be the most accurate representation of the data? 11, 11, 18, 32, 34, 115
Mode: 11
Median: 25
Mean: 36.8
Median would be most accurate because out of mode, median, and mean, median is closer to all of the numbers than mode and mean
Answer:
Median would probably give the most accurate representation
Median = 25
Step-by-step explanation:
The three main measures of central tendency are mean, mode and median.
The mean is the sum of all terms divided by the number of terms:
\(Mean = \frac{x11+11+18+32+34+115}{6} = 36.83\)
Since there is a large deviation within the values in the data set, the mean is not an accurate representative fot this case.
The mode is value that appears the most in a data set. The mode in this problem is 11; this value doesn't appear enough in the data set for it to be considered an accurate representation of the data.
The median is the central value of the set; since there is an even number of values, the median will be the average of the 2 central values:
\(Median = \frac{18+32}{2} =25\)
When compared to the other measures, the median is the one with the lesser deviation from all values within the set and, therefore, would probably give the most accurate representation.