For a distribution, the first four moments about the origin are -1.3, 15, -26 and 102. The third moment about the mean is: 

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SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)
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  1. 28.1
  2. 27.9
  3. 21.9
  4. 25.6

Answer (Detailed Solution Below)

Option 1 : 28.1
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The correct answer is 28.1
Key Points

The first, second, third and fourth moments about the mean are given as \(\mu_1 =(-1.3), \mu_2=15, \mu_3=(-26), \mu_4=102\); where \(\mu_1 = 0\)\(\mu_2 = \mu'_2 - (\mu'_1)^2\), and, \(\mu_3 = \mu'_3 - 3\mu'_2\mu'_1 + 2(\mu'_1)^3\)Therefore, plugging the information into the equation of the third moment about the mean, we have 
\(\mu_3 = \mu'_3 - 3\mu'_2\mu'_1 + 2(\mu'_1)^3\)
or, \(\mu_3 = (-26) - 3 \times 15 \times (-1.3) + 2(-1.3)^3\)
or, \(\mu_3 = -26 + 58.5 -4.394\)
or, \(\mu_3 \approx 28.1\)
Hence, the third moment about the mean is 28.1

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