Question 1 0 Obtain the mean of the following distribution- begin array - c - c - Whine4 - 4 Whline 8 - 6 Nhline14 - 8 Whline11 - 10 Wlhline3 - 12 Whline array

We know that, Mean of the data (x̅) = ∑_i=1^5f_i x_i/∑_i=1^5f_i = f_1 x_1 + f_2 x_2 + f_3 x_3 + f_4 x_4 + f_5 x_5/f_1 + f_2 + f_3 + f_4 + f_5 =4 × 4 + 8 × 6 + ...

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Standard X

Mathematics

Relation between Mean of Step- Deviations (U) and Mean

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Question 10
Obtain the mean of the following distribution.

$\begin{matrix} Frequency (f_{i}) & Variable (x_{i}) 4 & 4 8 & 6 14 & 8 11 & 10 3 & 12 \end{matrix}$

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Solution

We know that,
Mean of the data $(¯ x) = \frac{\sum_{i = 1}^{5} f_{i} x_{i}}{\sum_{i = 1}^{5} f_{i}} = \frac{f_{1} x_{1} + f_{2} x_{2} + f_{3} x_{3} + f_{4} x_{4} + f_{5} x_{5}}{f_{1} + f_{2} + f_{3} + f_{4} + f_{5}}$

$= \frac{4 \times 4 + 8 \times 6 + 14 \times 8 + 11 \times 10 + 3 \times 12}{4 + 8 + 14 + 11 + 3}$

$\frac{16 + 48 + 112 + 110 + 36}{40} = \frac{322}{40} = 8.05$

Hence, the mean of the given data is 8.05.

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Q. Question 10
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Question 10 Obtain the mean of the following distribution. Frequency(fi)Variable(xi)44861481110312

We know that, Mean of the data (¯x)=∑5i=1fixi∑5i=1fi=f1x1+f2x2+f3x3+f4x4+f5x5f1+f2+f3+f4+f5 =4×4+8×6+14×8+11×10+3×124+8+14+11+3 16+48+112+110+3640=32240=8.05 Hence, the mean of the given data is 8.05.

Question 10
Obtain the mean of the following distribution.

$\begin{matrix} Frequency (f_{i}) & Variable (x_{i}) 4 & 4 8 & 6 14 & 8 11 & 10 3 & 12 \end{matrix}$