i)
Mean
"\\bar{x}= \\frac{\\sum f(x) \\times x}{\\sum f(x)} \\\\\n\n= \\frac{30700}{85} \\\\\n\n=361.17"
ii)
Population SD
"\\sigma = \\sqrt{ \\frac{(\\sum f(x) \\times x^2) - \\frac{(\\sum f(x) \\times x)^2}{n} }{n} } \\\\\n\n\\sqrt{ \\frac{12105000 - \\frac{(30700)^2}{85} }{85} } \\\\\n\n= \\sqrt{11963.3218} \\\\\n\n= 109.3776"
Population standard deviation is $109.37. There is about $109.37 deviate the amount from mean value.
iii)
Population skewness
"SK = \\frac{\\sum (x_i - \\bar{x})^3}{n \\times \\sigma^3} \\\\\n\n= \\frac{35680604.53}{85 \\times (109.37)^3} \\\\\n\n= 0.320"
Since SK>0 the distribution slightly negatively skewed.
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