Calculate the mean of the following data- using direct method- - Class 25-35 35-45 45-55 55-65 65-75- Frequency 6 10 8 12 4- -

Class Frequency (f_i) Mid Values (x_i) (∑ f_ix_i) 25 35 6 30 180 35 45 10 40 400 45 55 8 ...

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Standard X

Mathematics

Direct Method of Finding Mean

Calculate the...

Question

Calculate the mean of the following data, using direct method:
$\begin{matrix} Class & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 Frequency & 6 & 10 & 8 & 12 & 4 \end{matrix}$

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Solution

Class Frequency ( $f_{i}$ ) Mid Values ( $x_{i}$ ) ( $\sum f_{i} x_{i}$ )

25 - 35 6 30 180

35 - 45 10 40 400

45 - 55 8 50 400

55 - 65 12 60 720

65 - 75 4 70 280

Total $\sum f_{i}$ =40 $\sum f_{i} x_{i}$ =1980

Therefore, Mean, $¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$

= 1980/40 = 49.5

Therefore, $¯ x$ = 49.5

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Class	Frequency ( $f_{i}$ )	Mid Values ( $x_{i}$ )	( $\sum f_{i} x_{i}$ )
25 - 35	6	30	180
35 - 45	10	40	400
45 - 55	8	50	400
55 - 65	12	60	720
65 - 75	4	70	280
Total	$\sum f_{i}$ =40		$\sum f_{i} x_{i}$ =1980

Calculate the mean of the following data, using direct method: Class25−3535−4545−5555−6565−75Frequency6108124

Class Frequency (fi) Mid Values (xi) (∑fixi) 25 - 35 6 30 180 35 - 45 10 40 400 45 - 55 8 50 400 55 - 65 12 60 720 65 - 75 4 70 280 Total ∑fi=40 ∑fixi=1980 Therefore, Mean, ¯x=∑fixi∑fi = 1980/40 = 49.5 Therefore, ¯x = 49.5

Calculate the mean of the following data, using direct method:
$\begin{matrix} Class & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 Frequency & 6 & 10 & 8 & 12 & 4 \end{matrix}$