Average of 6 distinct natural numbers is 49.If the average of the three largest numbers is found to be 57, then find the difference of the highest and the lowest possible median of these numbers?
Answers
Answer:
Let say the Number be (a, b, c, d, e, f) and these are in increasing order, whose average is given as 49.
Sum of the numbers = 49 × 6 = 294
Average of three largest numbers is 57, and we have three largest number as d, e, and f
Now we are going to find highest and lowest possible median of these numbers.
Highest Possible Median
⇒ a, b, c, d, e, f
- we can take e = 57 as it's the average of three largest number
⇒ a, b, c, d, 57, f
- To find Median of these numbers we have to add Middle two terms and divide it by 2, that's why we will put highest possible number for c and d
- Value of c and d should must be less than 57 whereas value of f should must be greater than 57
⇒ a, b, 55, 56, 57, 58
- Let's check whether it satisfy the sum or not ; (a + b + 55 + 56 + 57 + 58) = 294
- (a + b + 226) = 294
- (a + b) = (294 - 226)
- (a + b) = 68
- Value of a and b won't come in negative, so this satisfy the Highest Possible Numbers.
⇢ Highest Possible Median = (c + d)/2
⇢ Highest Possible Median = (55 + 56)/2
⇢ Highest Possible Median = 111/2
⇢ Highest Possible Median = 55.5
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Lowest Possible Median
⇒ a, b, c, d, e, f
- we can take e = 57 as it's the average of three largest number
⇒ a, b, c, d, 57, f
- To find Median of these numbers we have to add Middle two terms and divide it by 2, that's why we will put lowest possible number for c and d
- Value of c and d should must be greater than a and b
⇒ 1, 2, 3, 4, 57, f
⇢ Lowest Possible Median = (c + d)/2
⇢ Lowest Possible Median = (3 + 4)/2
⇢ Lowest Possible Median = 7/2
⇢ Lowest Possible Median = 3.5
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• According to the Question :
⇒ (Highest – Lowest) Possible Median
⇒ 55.5 – 3.5
⇒ 52
∴ Hence, the required answer is 52.
Answer:
yes the above calculation is positively correct