the histograms below show the ages of dogs at four different shelters. For which set of data is the mean most likely greater than the median?
Answers
This is a question of Statistics.
First, we are going to define Mean and Median.
Mean: Mean can also be termed as the average value. We obtain MEAN by dividing the Sum of all values by total Number of values
For Example: 2, 5, 6, 7, 10 There are 5 values
Mean = (2+5+6+7+10)/5 = 6
Median: Median is the middle value. We arrange the data in Ascending or Descending order first to find the median.
⇒ There is 1 middle value for ODD number of Data.
2, 5, 6, 7, 10 has ONE middle value and that is 6
⇒ There are 2 middle values for even number of Data.
2, 5, 6, 7, 9, 10 has TWO middle values and that are 6 & 7.
⇒ Mean is always greater in Data set where there are outliers. Outliers are the end values that affect the result of the Mean.
For Example: 2, 5, 6, 7, 10
Mean = (2+5+6+7+10)/5 = 6
And it has Median 6 (The Middle Value)
BUT
If we change the last term 10 by 30, then there will beno change in MEDIAN. 2, 5, 6, 7, 30
Median is still 6
But Mean = (2+5+6+7+10)/5 = 10
In this case 30 is the Outlier that has affected the Mean.
And Mean becomes greater than the Median.
So look for the DATA set with OUTLIERS. That data-set will have greater MEAN.
Answer:
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