Less than , more than ogive

Chapter 14 Class 10 Statistics
Concept wise

Here, we list all formulas that are required for Class 9 and 10 Exams

The formula list includes

• Range
• Mean
• Mean of Raw Data
• Mean of Discrete Data
• Mean of Grouped Data
• Median
• Median of Raw Data
• Median of Discrete Data
• Median of Grouped Data
• Mode
• Mode of Raw Data
• Mode of Discrete Data
• Mode of Grouped Data

Β

## Range

Range = Maximum value β Minimum Value

Β

For data

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

Β

Maximum value = 32

Minimum value = 2

Β

Thus,

Range = 32 β 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,

Β and their intersection is the median

## Mode of Raw, Discrete and Grouped Data

Β

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### 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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.