Find the missing frequency $k$ if mean deviation about mean for the given data is $0.91$ $x$ $3.5$ $4.5$ $5.5$ $6.5$ $7.5$ $8.5$ $9.5$ $f$ $k$ $7$ $22$ $60$ $85$ $32$ $8$

The total number of observations is calculated as k + 7 + 22 + 60 + 85 + 32 + 8, which equals k + 214. Calculating the total sum as 3.5k + 341.5 and the mean by dividing by N gives an estimated mean of roughly 7.25. The mean deviation formula uses the sum of absolute deviations from this mean divided by N, which equals 0.91. Multiplying 0.91 by the total frequency (k + 214) gives the sum of absolute deviations; solving the resulting linear equation for k yields k = 3. The missing frequency k is 3.

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