If A=900, `Sigmaf_(i)d_(l)=-400` and `Sigmaf_(i=100`, then what is the value of `bar(x)` ?

Answer

To find the value of \(\bar{x}\) (the mean), we can use the formula:

\[ \bar{x} = A + \bar{d} \]

Where:
- \(A\) is the assumed mean,
- \(\bar{d}\) is the average of the deviations, calculated as \(\frac{\Sigma f_i d_i}{\Sigma f_i}\).

Given:
- \(A = 900\)
- \(\Sigma f_i d_i = -400\)
- \(\Sigma f_i = 100\)

### Step 1: Calculate \(\bar{d}\)
Using the formula for \(\bar{d}\):

\[ \bar{d} = \frac{\Sigma f_i d_i}{\Sigma f_i} \]

Substituting the given values:

\[ \bar{d} = \frac{-400}{100} = -4 \]

### Step 2: Calculate \(\bar{x}\)
Now substitute \(\bar{d}\) back into the mean formula:

\[ \bar{x} = A + \bar{d} \]

Substituting \(A = 900\) and \(\bar{d} = -4\):

\[ \bar{x} = 900 + (-4) = 900 - 4 = 896 \]

### Final Answer:
\(\bar{x} = 896\)

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