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Answer :
We are given the formula for the mean of grouped data when using an assumed mean. The formula is:
[tex]$$
\overline{x} = A + \frac{\Sigma f d}{\Sigma f}
$$[/tex]
where:
- [tex]$\overline{x}$[/tex] is the actual mean,
- [tex]$A$[/tex] is the assumed mean,
- [tex]$\Sigma f$[/tex] is the total frequency, and
- [tex]$\Sigma f d$[/tex] is the sum of the products of the frequency and the deviation.
To find [tex]$\Sigma f d$[/tex], we rearrange the formula as follows:
[tex]$$
\Sigma f d = \Sigma f \times (\overline{x} - A)
$$[/tex]
Substitute the given values:
- [tex]$\overline{x} = 80$[/tex]
- [tex]$A = 60$[/tex]
- [tex]$\Sigma f = 40$[/tex]
Calculate the difference between the actual mean and the assumed mean:
[tex]$$
\overline{x} - A = 80 - 60 = 20
$$[/tex]
Now multiply this difference by the total frequency:
[tex]$$
\Sigma f d = 40 \times 20 = 800
$$[/tex]
Thus, the value of [tex]$\Sigma f d$[/tex] is [tex]$\boxed{800}$[/tex].
[tex]$$
\overline{x} = A + \frac{\Sigma f d}{\Sigma f}
$$[/tex]
where:
- [tex]$\overline{x}$[/tex] is the actual mean,
- [tex]$A$[/tex] is the assumed mean,
- [tex]$\Sigma f$[/tex] is the total frequency, and
- [tex]$\Sigma f d$[/tex] is the sum of the products of the frequency and the deviation.
To find [tex]$\Sigma f d$[/tex], we rearrange the formula as follows:
[tex]$$
\Sigma f d = \Sigma f \times (\overline{x} - A)
$$[/tex]
Substitute the given values:
- [tex]$\overline{x} = 80$[/tex]
- [tex]$A = 60$[/tex]
- [tex]$\Sigma f = 40$[/tex]
Calculate the difference between the actual mean and the assumed mean:
[tex]$$
\overline{x} - A = 80 - 60 = 20
$$[/tex]
Now multiply this difference by the total frequency:
[tex]$$
\Sigma f d = 40 \times 20 = 800
$$[/tex]
Thus, the value of [tex]$\Sigma f d$[/tex] is [tex]$\boxed{800}$[/tex].
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