The mean of 10 numbers is 50. Removing one of the numbers causes the mean to decrease to 45. What number was removed?
Answers
Answer:
The number removed is 95.
Step-by-step Explanation
To Find :-
- The number removed.
★ Solution :-
The mean of 10 numbers is = 50 .
Removing one of the numbers, the mean to decreases to = 45 .
Let the numbers be n₁, n₂, n₃, n₄, n₅, n₆, n₇, n₈, n₉ and n₁₀ .
As we know that,
Mean = Sum of all numbers/Total number of Numbers
Therefore,
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉+n₁₀)/10 = 50
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉+n₁₀) = 50 × 10
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉+n₁₀) = 500
∴ The sum of ten numbers is 500.
Now, After removing one Number :-
➝ Removing n₁₀
➝ After removing a number, the total numbers will be 9.
Hence,
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉)/9 = 45
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉) = 45 × 9
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉) = 45 × 9
→ (n₁+n₂+n₃+n₄+n₅+n₆+n₇+n₈+n₉) = 405
∴ The sum of nine numbers is 405.
According the question,
The number removed is :-
→ Number removed = Sum of 10 numbers - Sum of 9 numbers
→ 500 - 405
→ 95
Hence, The required number is 95.
Step-by-step explanation:
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