Find an estimate of the combined variance of the following data for the marks obtained in a test by 88 students. Marks (x) $0 \le x < 10$ $10 \le x < 20$ $20\le x < 30$ $30\le x < 40$ $40 \le x < 50$ Frequency (f) 6 16 24 25 17

To find variance, calculate the mean first using midpoints (5, 15, 25, 35, 45). Mean = (6*5 + 16*15 + 24*25 + 25*35 + 17*45) / 88 = 2520 / 88 = 28.636. Variance = sum(f * (x - mean)^2) / N. Calculations: 6*(5-28.6)^2 + 16*(15-28.6)^2 + 24*(25-28.6)^2 + 25*(35-28.6)^2 + 17*(45-28.6)^2 = 3335 + 2967 + 311 + 1024 + 4573 = 12210. Variance = 12210 / 88 = 138.75. Option C is the closest.