Here, we list all Statistics Formulas for your use.

The formula list includes

## Range

Range = Maximum value – Minimum Value

For data

5, 10, 15, 18, 21, 24, 24, 13, 2, 9, 9, 18, 18, 32, 28, 3, 14, 25, 3, 27

Maximum value = 32

Minimum value = 2

Thus,

Range = 32 – 2 = 30

## Median of Raw, Discrete and Grouped Data

We can also find median using Ogive curve

We draw less than and more than ogive,

and their intersection is the median

## Coefficient of Variation

1. Chapter 15 Class 11 Statistics
2. Concept Wise
3. Co-efficient of variation

Transcript

Mean of Raw Data π₯ Μ = (ππ’π ππ πππ πππ£ππ‘ππππ )/(ππ’ππππ ππ πππ πππ£ππ‘ππππ ) Mean of Discrete Data π₯ Μ = (ββγπ_π π₯_π γ)/(ββπ_π ) Mean of Grouped Data Direct Method π₯_π = (πππππ ππππ π  πππππ‘ + πΏππ€ππ ππππ π  πππππ‘)/2 Mean = π₯ Μ = (ββγπ_π π₯_π γ)/(ββπ_π ) Assumed Mean Method a β middle value of π₯_π column π_π = π₯_π β a Mean = π₯ Μ = a + (ββγπ_π π_π γ)/(ββπ_π ) Step-Deviation Method π’_π = (π₯_π β π)/β h β class size Mean = π₯ Μ = a + (ββγπ_π π’_π γ)/(ββπ_π ) Γ h Median Median of Raw Data Write data in ascending/descending order N = Total Number of observations (i) If N is odd Median = ((π + 1)/2)^π‘β observation (ii) If N is even Median = ((π/2)^π‘β πππ πππ£ππ‘πππ + (π/2 + 1)^π‘β πππ πππ£ππ‘πππ)/2 Median of Discrete Data First, we find cumulative frequency (cf) Then, we find π/2 N = Total number of observations (i) If N is odd Median = Observation where cf is greater than π/2 (ii) If N is even (π/2)^π‘β πππ πππ£ππ‘πππ = Observation where cf is equal to π/2 (π/2 + 1)^π‘β πππ πππ£ππ‘πππ = Observation where cf is greater than π/2 Median = ((π/2)^π‘β πππ πππ£ππ‘πππ + (π/2 + 1)^π‘β πππ πππ£ππ‘πππ)/2 Median of Grouped Data We use the formula Median = l + ((π/2 β ππ))/π Γ h where Median class = class with cumulative frequency greater than π/2 l = lower limit of median class h = class size f = frequency of median class cf = cumulative frequency of class preceding median class Mode Mode of Raw Data We follow these steps Arrange in ascending or descending order Find the element occurring max number of times β΄ Mode = Element occurring maximum number of times Mode of Discrete Data Mode is the data which occurs maximum number of times, β΄ Mode = Data with maximum frequency (fi) Mode of Grouped data We use the formula Mode = l + ((π_1β π_0)/(2 π_1 β π_(0 )β π_2 )) Γ h where Modal Class = Class with highest frequency l = lower limit of modal class f = frequency of modal class π_0 = frequency of class preceding modal class π_2 = frequency of class succeeding modal class h = class size Mean deviation of Raw Data Raw data is like π₯_1, π₯_2, π₯_3, β¦ β¦ π₯_π Mean Deviation About Mean = 1/π β_(π=1)^πβγ|π₯_π β π₯ Μ|γ where π₯ Μ = mean Mean Deviation About Median = 1/π β_(π=1)^πβγ|π₯_π βπ|γ where M = Median Mean deviation of Discrete Data Discrete data looks like x x1 x2 x3 x4 x5 . . . xn f f1 f2 f3 f4 f5 . . . fn Mean Deviation about mean = 1/π β_(π = 1)^πβγπ_π |π₯_π β π₯ Μ|γ where N = β_(π = 1)^πβπ_π and π₯ Μ = mean = (ββγπ_π π₯_π γ)/(ββπ_π ) Mean Deviation about median = 1/π β_(π = 1)^πβγπ_π |π₯_πβπ|γ where N = β_(π = 1)^πβπ_π and M = Median Mean deviation of grouped continuous data Mean Deviation About Mean π₯_π = (πππππ πππππ‘ ππ ππππ π  + πΏππ€ππ πππππ‘ ππ ππππ π )/2 Mean deviation about mean = 1/π β_(π = 1)^πβγπ_π |π₯_π β π₯ Μ|γ where N = β_(π = 1)^πβπ_π and π₯ Μ = mean We can find mean by normal method or step-deviation method Mean Deviation about median = 1/π β_(π = 1)^πβγπ_π |π₯_πβπ|γ where N = β_(π = 1)^πβπ_π and M = Median = l + ((π/2 β πΆ)/π) Γ h Variance and Standard Deviation for raw data Variance π^2 = 1/π β_(π = 1)^πβ(π₯_πβπ₯ Μ )^2 where π₯ Μ = mean Standard deviation π = βππππππππ π = β(1/π (ββ(π₯_πβπ₯ Μ )^2 )) where π₯ Μ = mean Variance and Standard deviation for Discrete Frequency Distribution Standard deviation (π) = β(1/π ββγπ_π (π₯_πβπ₯ Μ )γ^2 ) where π₯ Μ = mean N = β_(π = 1)^πβπ_π Note:- Variance = (ππ‘ππππππ π·ππ£πππ‘πππ)^2 Variance and Standard deviation for Grouped Frequency Distribution We can use different methods to find Standard Deviation Normal method to find Standard deviation Standard deviation (π) = β(1/π ββγπ_π (π₯_πβπ₯ Μ )^2 γ) where π₯ Μ = mean N = β_(π = 1)^πβπ_π Another method to find Standard Deviation π = 1/π β(πββγπ_π γπ₯_πγ^2 γβ(ββγπ_π π₯_π γ)^2 ) where N = β_(π = 1)^πβπ_π Shortcut method to find Standard Deviation π = β/π β(πββγπ_π γπ¦_πγ^2 γβ(ββγπ_π π¦_π γ)^2 ) where π¦_π = (π₯_π β π)/β a = Assumed mean (the middle most value of xi) N = β_(π = 1)^πβπ_π Coefficient of Variation Coefficient of variation (C.V) = π/π₯ Μ Γ 100 where π β standard deviation π₯ Μ β mean Less C.V means more consistent data

Co-efficient of variation