Question

Class 10

Mathematics

Chapter 14 - Statistics

Formulas Needed

Quality Answer Needed​

Answer 1

Answer:

Required Answer :-

Lets see the formula

$\sf \: mean \: = \bar{x} = \dfrac{ \sum \: x}{n}$

$\sf \: Median_{odd} = \bigg( \dfrac{n + 1}{2} \bigg)$

$\sf \: Median _{even} = \dfrac{n}{2}$

Mode = Which value occur most

$\sf \: variance \: = \sigma {}^{2} = \dfrac{ {\sum(x - \bar{x})}^{2} }{n}$

Standard Derivation :-

$\sf \sigma \: = \sqrt{ \dfrac{ \sum(x - \bar{x}) {}^{2} }{n} }$

Answer 2

Required Formulas :

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1. Mean of the group data:

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(i) The Direct method forming is given by,

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$\sf{:\implies Mean (\bar{x}) = \dfrac{\sum f_i x_i}{\sum f_i}}$

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(ii) The Assume-mean method forming is given by,

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$\sf{:\implies Mean (\bar{x}) = a + \dfrac{\sum f_i d_i}{\sum f_i}}$

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(iii) The Step-deviation method formula is given by,

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$\sf{:\implies Mean (\bar{x}) = a + \bigg\lgroup\dfrac{\sum f_i u_i}{\sum f_i}\bigg\rgroup \times h}$

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2. Mode of the group data:

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The mode formula is given by,

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$\sf{:\implies Mode (M_o) = l + \bigg\lgroup \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\bigg\rgroup \times h}$

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3. Median of the group data:

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The median formula is given by,

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$\displaystyle\sf{:\implies Median (M_e) = l + \bigg\lgroup \frac{ \frac{n}{2} - cf}{f} \bigg \rgroup \times h}$

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4. Empirical formula:

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The Empirical formula is given by,

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$\sf{:\implies 3Median = Mode + 2Mean}$

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