Check sibling questions

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 – 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 – 2 = 30

Β 

Mean of Raw, Discrete and Grouped Data

Mean of Raw, Discrete and Grouped Data.jpg

Median of Raw, Discrete and Grouped Data

Statistics Formulas for Class 9 and 10 - Part 2

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

Statistics Formulas for Class 9 and 10 - Part 3

Β 


Transcript

Mean of Raw Data π‘₯ Μ… = (π‘†π‘’π‘š π‘œπ‘“ π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘›π‘ )/(π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘›π‘ ) Mean of Discrete Data π‘₯ Μ… = (βˆ‘β–’γ€–π‘“_𝑖 π‘₯_𝑖 γ€—)/(βˆ‘β–’π‘“_𝑖 ) Mean of Grouped Data Direct Method π‘₯_𝑖 = (π‘ˆπ‘π‘π‘’π‘Ÿ π‘π‘™π‘Žπ‘ π‘  π‘™π‘–π‘šπ‘–π‘‘ + πΏπ‘œπ‘€π‘’π‘Ÿ π‘π‘™π‘Žπ‘ π‘  π‘™π‘–π‘šπ‘–π‘‘)/2 Mean = π‘₯ Μ… = (βˆ‘β–’γ€–π‘“_𝑖 π‘₯_𝑖 γ€—)/(βˆ‘β–’π‘“_𝑖 ) Assumed Mean Method a β†’ middle value of π‘₯_𝑖 column 𝑑_𝑖 = π‘₯_𝑖 βˆ’ a Mean = π‘₯ Μ… = a + (βˆ‘β–’γ€–π‘“_𝑖 𝑑_𝑖 γ€—)/(βˆ‘β–’π‘“_𝑖 ) Step-Deviation Method 𝑒_𝑖 = (π‘₯_𝑖 βˆ’ π‘Ž)/β„Ž h β†’ class size Mean = π‘₯ Μ… = a + (βˆ‘β–’γ€–π‘“_𝑖 𝑒_𝑖 γ€—)/(βˆ‘β–’π‘“_𝑖 ) Γ— h Median Median of Raw Data Write data in ascending/descending order N = Total Number of observations (i) If N is odd Median = ((𝑁 + 1)/2)^π‘‘β„Ž observation (ii) If N is even Median = ((𝑁/2)^π‘‘β„Ž π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘› + (𝑁/2 + 1)^π‘‘β„Ž π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘›)/2 Median of Discrete Data First, we find cumulative frequency (cf) Then, we find 𝑁/2 N = Total number of observations (i) If N is odd Median = Observation where cf is greater than 𝑁/2 (ii) If N is even (𝑁/2)^π‘‘β„Ž π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘› = Observation where cf is equal to 𝑁/2 (𝑁/2 + 1)^π‘‘β„Ž π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘› = Observation where cf is greater than 𝑁/2 Median = ((𝑁/2)^π‘‘β„Ž π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘› + (𝑁/2 + 1)^π‘‘β„Ž π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘–π‘œπ‘›)/2 Median of Grouped Data We use the formula Median = l + ((𝑛/2 βˆ’ 𝑐𝑓))/𝑓 Γ— h where Median class = class with cumulative frequency greater than 𝑁/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 ∴ Mode = Element occurring maximum number of times Mode of Discrete Data Mode is the data which occurs maximum number of times, ∴ Mode = Data with maximum frequency (fi) Mode of Grouped data We use the formula Mode = l + ((𝑓_1βˆ’ 𝑓_0)/(2 𝑓_1 βˆ’ 𝑓_(0 )βˆ’ 𝑓_2 )) Γ— h where Modal Class = Class with highest frequency l = lower limit of modal class f = frequency of modal class 𝑓_0 = frequency of class preceding modal class 𝑓_2 = frequency of class succeeding modal class h = class size

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.