Question:

Given data 60,60,44,58,68,α,β,5660, 60, 44, 58, 68, α, β, 56 has mean 5858, variance = 66.266.2, then find α2+β2α^2 + β^2.

Updated On: Feb 15, 2024
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Solution and Explanation

The formula for Variance is:\text{The formula for Variance is:} x2n(xˉ)2\frac{\sum x^2}{n}-(\bar x)^2

Substituting the data given in the question, we find,\text{Substituting the data given in the question, we find,}

7200+1936+3364+4624+3136+α2+β283364\frac{7200+1936+3364+4624+3136+\alpha^2+\beta^2}{8}-3364 =66.2=66.2

2532.5+α2+β283364=66.22532.5+\frac{\alpha^2+\beta^2}{8}-3364=66.2

=7181.6=7181.6 7182\approx7182

The correct answer is 7182.\text{The correct answer is 7182.}

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Concepts Used:

Variance and Standard Deviation

Variance:

According to layman’s words, the variance is a measure of how far a set of data are dispersed out from their mean or average value. It is denoted as ‘σ2’.

Variance Formula:

Read More: Difference Between Variance and Standard Deviation

Standard Deviation:

The spread of statistical data is measured by the standard deviation. Distribution measures the deviation of data from its mean or average position. The degree of dispersion is computed by the method of estimating the deviation of data points. It is denoted by the symbol, ‘σ’.

Types of Standard Deviation:

  • Standard Deviation for Discrete Frequency distribution
  • Standard Deviation for Continuous Frequency distribution

Standard Deviation Formulas:

1. Population Standard Deviation

2. Sample Standard Deviation