The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :

Using the mean formula, the sum of the five observations is 5 multiplied by 5, which equals 25. Let the two unknown observations be a and b; so 1 + 3 + 8 + a + b = 25, meaning a + b = 13. The variance formula gives the sum of squared deviations as 9.20 multiplied by 5, which is 46; therefore, the sum of squares of the observations equals 46 plus 5 times the square of the mean (25), giving 171. So 1 + 9 + 64 + a squared + b squared = 171, which simplifies to a squared + b squared = 97. Substituting b = 13 minus a gives a squared + (13 minus a) squared = 97, which simplifies to the quadratic equation 2a squared minus 26a + 72 = 0, or a squared minus 13a + 36 = 0. Solving this yields the values 4 and 9 for the two missing observations, so their ratio is 4 to 9.

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