Calculate the mean of the following using an assume mean of 600. 635, 725, 439, 710, 694, 720, 450, 625, 392

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ScanSolve AI Tutor · Accepted Answer

Here's how to calculate the mean using an assumed mean of 600:

Identify the assumed mean (A) and the data points ( $x_i$ ).
The assumed mean is $A = 600$ .
The data points are $x_i = \{635, 725, 439, 710, 694, 720, 450, 625, 392\}$ .
The number of data points is $n = 9$ .
Calculate the deviation ( $d_i = x_i - A$ ) for each data point.
$\begin{align*} d_1 &= 635 - 600 = 35 \\ d_2 &= 725 - 600 = 125 \\ d_3 &= 439 - 600 = -161 \\ d_4 &= 710 - 600 = 110 \\ d_5 &= 694 - 600 = 94 \\ d_6 &= 720 - 600 = 120 \\ d_7 &= 450 - 600 = -150 \\ d_8 &= 625 - 600 = 25 \\ d_9 &= 392 - 600 = -208 \end{align*}$
Calculate the sum of the deviations ( $\sum d$ ).
$\sum d = 35 + 125 - 161 + 110 + 94 + 120 - 150 + 25 - 208 = -60$
Apply the formula for the mean using the assumed mean method.
The formula is $\bar{x} = A + \frac{\sum d}{n}$ .
$\bar{x} = 600 + \frac{-60}{9}$
Simplify the expression to find the mean.
$\bar{x} = 600 - \frac{60}{9} \\ \bar{x} = 600 - 6.666... \\ \bar{x} \approx 593.33$
The mean of the given data is approximately $\text{593.33}$ .

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