Statistics-Class-10-Opt. Maths (2+4+4=10 Marks)

Author:
AMBIK BARAL
Topic:
Statistics

Introduction

Quartile Deviation (Q.D.)
  • The difference between the upper quartile and the lower quartile is called INTERQUARTILE RANGE.
  • The semi-interquartile range of the data is known as Quartile Deviation(Q.D.)
  • Here ,inter-quartile range
  • Semi- interquartile range
  • Coefficient of quartile deviation
For continuous or grouped data
  • Where, lower limit of quartile class c.f. of the preceding class frequency of quartile class class -height or, class - size or class interval

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Find quartile deviation and its coefficient from the following data.

  1. [ Ans: 12.17, 0.49]
  2. [Ans: 3.06, 0.21 ]
  3. [ Ans: 23.5, 0.35]
  4. [Ans: 1.99, 0.21]
  5. [ Ans: 3.44, 0.22 ]

Introduction

Mean Deviation The average of the absolute values of the deviation of each item from mean, median or mode is known as a mean deviation. It is also known as average deviation. It is denoted by M.D. Calculation of Mean Deviation For continuous series
  1. M.D. from mean
  2. M.D. from median
  3. Coefficient of M.D. from mean
  4. Coefficient of M.D. from median Where,

Standard Deviation

Standard deviation is the positive square root of the arithmetic mean of the square of deviations of given data taken from mean. It is also known as "Root mean square deviation". It is denoted by Greek letter (read as sigma). It is considered as the best measure of dispersion because:
  1. It's value is based on all the observations.
  2. Deviation of each term is taken from the central value.
  3. All algebraic sign are also considered
Calculation of Standard Deviation Actual mean method: Standard deviation(σ), where is the mid-value of each class-interval. Direct method: Standard deviation(σ) , is the where is the mid-value of each class-interval. Assumed mean method: Standard deviation(σ) , where, , Step deviation method: When the class-interval is very large then step deviation method is used to find the standard. Standard deviation(σ) Where Coefficient of variation (C.V.) The relative measure of standard deviation is known as the coefficient of standard deviation and is defined by Coefficient of standard deviation If the coefficient of standard deviation is multiplied by 100, then it is known as coefficient of variation. Coefficient of variation is denoted by C.V. and is calculated as:    Greater the coefficient of variation, greater will be the variation and less will be the consistency or uniformity. Less the C.V., greater will be the consistency or uniformity. For the consistency or uniformity of distribution, we use the C.V. So, C.V. is used to compare given distributions. Variance: The square of standard deviation(σ) is called variation. It is given by       
  1. Find the standard deviation of the following data.[SEE 2075 R', SEE 2073 S'] [Ans: 11.49]
  2. Find the standard deviation of the following data.[ 2070 S ] [Ans: 6.05 ]
  3. Find the standard deviation and its coefficient of the given data.[ 2069 R'] [ Ans: 11.66, 0.35 ]
  4. Calculate the coefficient of variation from the data given below.[ 2075 R ] [ Ans: 44.1% ]
  5. Find the standard deviation and coefficient of variation from the given data. [ SEE MODEL 2076 ] [Ans: 6.05 & 50.42 % ]

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