Respuesta :
Mean, median and mode are 3 of the central measures of a data set. Its central measures are: Mean = 81.07 , Median = 83 , Mode = 89. The best measure of center for this data set is its mode = 89
- Mean: -
Mean is the arithmetic average. In other words, sum all data values and divide that sum by the number of its values.
- Mode: -
Mode is that value from the data set which occurred the most in the data set. In other words, sometimes there can be more than 2 values, and sometimes this mode is find by a different technique.
- Median: -
Median is a value before which and after which lies same number of data observations (sorted data either arranged ascending or descending.
For the given data set:
80, 84, 79, 44, 87, 73, 89, 90, 82, 89, 93, 97, 77, and 71,
Sorting the data in ascending order, the data set looks like:
44, 71, 73, 77, 79, 80, 82, 84, 87, 89, 89, 90, 93, 97
Its mean is:
Mean = sum of data values/ number of data values
= 1135/14 ≈ 81.07
The number 89 occurs 2 times, and rest of the numbers occur only one time. Thus, 89 occurs most frequently. Thus, its mode is 89.
There are 14 values, and thus, 7th and 8th values are the middle values. They are 82 and 84. Any value between 82 and 84 is median as before it and after it will lie 7- 7 values. But, traditionally, and unbiasedly, we'll take their(of 82 and 84) average which is 83. Thus,
Median = 83
Thus, we have:
Mean of the data set = 81.07 approximately.
Median of the data set = 83
Mode of the data set = 89
Since most of the data lies on the right side, thus, mean is not a good choice (as it is affected by outlier and we have 44 as an outlier). In case of outliers, we will accept median or mode. Both are ok here as there is only single outlier. The presence of outlier is still affecting median but not mode. So mode is the best choice here as central measure.
Thus, The best measure of center for this data set is its mode = 89
Learn more about mean, median and mode:
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