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This isn't homework, I am boggling my head over it though.

I got all sorts of answers, just not the answer my book demands.

For what value of $x$ the mean of the given observations $2x - 5, x + 3, 7 - x, 5-x$ and $x + 9$ with frequencies $2,3,4,6$ and $1$ respectively is $4$?

I seriously cant solve this, help would be MUCH appreciated. Note: Please don't use any advanced statistics formula, we are still on the basics. Sum of $f_ix_i$ over sum of $f_i$ is all I can use.

Saurabh
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Aayush Agrawal
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1 Answers1

5

Hint: $$\text{mean = }\frac{\sum_{i=1}^n f_ix_i}{\sum_{i=1}^n f_i}$$ where $f_i$ is the frequency of $x_i$ event.

$$\frac{2(2x-5) + 3(x+3) + 4(7-x) +6(5-x) + (x+9)}{16}=4$$ $$4x-10+3x+9+28-4x+30-6x+x+9=64$$ $$-2x+66=64$$ $$x=1$$

Saurabh
  • 3,138
  • Thanks, but can you please give me a more detailed calculation? I already reached that part, but couldnt get -1 as the answer :/ a step-by-step answer can help me find my mistake. – Aayush Agrawal Sep 10 '12 at 16:11
  • Im sorry but thats actually not it..the book wants the answer to be -1 not positive 1 D: – Aayush Agrawal Sep 10 '12 at 16:20
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    @aayush may be book's ans is wrong or you have copied it wrongly. You can check by putting $x=1$ in that the equation. – Saurabh Sep 10 '12 at 16:26
  • Found a tiny mistake. In your solution you marked the final one(x + 9) as (x - 9) – Aayush Agrawal Sep 10 '12 at 16:29