6) 7 prime numbers have a mean of 10. The median is 11, the mode is 17, the IQR is 14 and the range is 15. Find all 7 numbers.
Answers
Given : 7 prime numbers have a mean of 10. The median is 11, the mode is 17,
IQR is 14
range is 15.
To Find : All 7 numbers
Solution:
7 prime numbers
The median is 11,
=> A B C 11 D E F
we have atleast 2 , 17 in D , E and F as 17 is mode
Hence E = 17
A B C 11 D 17 F
Quartile : 1st Quartile (n+1)/4 if n odd or n/4 if n even
3rd Quartile 3(n+1)/4 if n odd or 3n/4 if n even
Hence 2nd and 6th number
Q3 - Q1 = IQR = 14
E - B = 14 => 17 - B = 14 => B = 3
A 3 C 11 D 17 F
As Mean is 10 so sum = 70 and prime number are odd except 2
Hence sum of 7 odd numbers = odd so 2 must be one number
2 3 C 11 D 17 F
range is 15 => F - 2 = 15
=> F = 17
2 3 C 11 D 17 17
2 + 3 + C + 11 + D + 17 + 17 = 70
=> C + D = 20
3 + 17 = 20
7 + 13 = 20
Hence 2 possible solution
2 3 3 11 17 17 17
2 3 7 11 13 17 17
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