The mode of the following data is $85.7$. Find the missing frequency in it. Size Frequency 45-55 7 55-65 12 65-75 17 75-85 f 85-95 32 95-105 6 105-115 10

Using the formula for the mode of grouped data, Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] * h, where L is 85, f1 is 32, f0 is f, f2 is 6, and h is 10. Substituting the given mode of 85.7 results in the equation 85.7 = 85 + [(32 - f) / (64 - f - 6)] * 10. Solving 0.7 = [(32 - f) / (58 - f)] * 10 gives 4.06 - 0.07f = 32 - f, which simplifies to 0.93f = 27.9 and results in a missing frequency of 30.

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