Consider the following ANOVA table.

Source of variation Degrees of freedom The sum of Squares (SS) Mean SS F Ratio

Treatments a b c 5

Error 12 d 20

Total 15 540

The values of a, b, c and d are, respectively:

Question

Question

This question was previously asked in

SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)

Answer 1

The correct answer is 3, 300, 100 and 240
Key Points

From the ANOVA table, we have the following information:
- Degrees of freedom for Treatments (a) = 3 Degrees of freedom for Error (b) = d = 12 Degrees of freedom for Total (c) = 15 Sum of Squares (SS) for Treatments = 5 Total SS = 540
- To determine the missing values, we can calculate the remaining sums of squares:
- SS for Error = Total SS - SS for Treatments = 540 - 5 = 535
Now, let's calculate the Mean SS for Treatments and Mean SS for Error:
- Mean SS for Treatments = SS for Treatments / Degrees of freedom for Treatments = 5 / 3 = 1.67
- Mean SS for Error = SS for Error / Degrees of freedom for Error = 535 / 12 = 44.58
Therefore, the values for a, b, c, and d are:
- a = 3, b = 300 (Mean SS for Treatments multiplied by Degrees of freedom for Treatments: 1.67 * 3 = 5), c = 100 (Sum of Squares for Error: 535), d = 240 (Degrees of freedom for Error: 12)

Hence, the values of a, b, c and d are, respectively, 3, 300, 100, and 240.