Less than , more than ogive

Chapter 13 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

## 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

## Mode of Raw, Discrete and Grouped Data

### 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