Question 5: What do they tell us here about the shape of the distribution?
If the data were symmetrically distributed, we would expect about 2.5% of the observations to be less than the mean minus 2 standard deviations. For a variable which can only take positive values, we can deduce positive skewness where the standard deviation is bigger than half the mean. However, here the variable is excess insulation where negative values are possible and so we cannot deduce the shape of the distribution from these values.
All that mean = 2.3 togs and standard deviation = 3.4 togs tell us is where the middle of the distribution is at 2.3 togs and that most observations, about 95%, are between 2.3 – 2×3.4 = –4.5 togs and 2.3 + 2×3.4 = 9.1 togs.
Back to Exercise: Summarising Data.
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Last updated: 27 July, 2009.