Hence, the five positive integers are 2, 2, 4, 4, 13.
Mean- The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
Median-The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
Mode-The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.
According to the question , it can be concluded that the total no. of observations are 5.
So , Let n=5
Let the integers be a, b, c, d and e
The question says that mode(s) are 2 and 4.
This indicates that 2 and 4 both have occurred more than once , and both have same frequency since both are modes.
Since we have only 5 integers , and 2 and 4 both are modes , so both these numbers have possibility to occur only twice.
Hence , it becomes , a=2 , b=2 , c=4 , and d=4
Hence we can say that out of five required integers ,four of them are 2 and 4.
Further , we are given that mean is 5.
therefore , using formula:
Mean = Sum of Observations / Number of observations(n)
Mean= (a+b+c+d+e) / 5
5 = (2+2+4+4+e) / 5
5 = (12+e)/5
Multiplying both sides by 5 , we get :
25 = 12+e
e=25-12
Hence , e = 13
So, the five positive integers are 2, 2, 4, 4, 13.
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