Calculation of Mean and Median
------------------------
To calculate the mean deviation of weights about median, we need to calculate the median first. The median is the middle value of the data set when arranged in ascending order.

The weights and the number of persons in each weight category are given as follows:

Weight (1b) | No.of persons
----------- | -------------
131-140 | 3
141-150 | 8
151-160 | 13
161-170 | 15
171-180 | 6
181-190 | 5

To calculate the median, we need to find the cumulative frequency of the data set. The cumulative frequency is the sum of the frequencies up to a particular value.

Weight (1b) | No.of persons | Cumulative Frequency
----------- | ------------- | --------------------
131-140 | 3 | 3
141-150 | 8 | 11
151-160 | 13 | 24
161-170 | 15 | 39
171-180 | 6 | 45
181-190 | 5 | 50

The median is the value that corresponds to the cumulative frequency of n/2, where n is the total number of observations. In this case, n=50, so the median corresponds to the cumulative frequency of 25.

The cumulative frequency of 25 falls in the weight category of 161-170, so the median weight is 165.5 lbs.

Calculation of Mean Deviation
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The mean deviation is the average of the absolute deviations of each value from the median. To calculate the mean deviation, we need to find the deviations of each weight from the median.

Weight (1b) | No.of persons | Deviation from Median
----------- | ------------- | ---------------------
131-140 | 3 | 34.5
141-150 | 8 | 24.5
151-160 | 13 | 14.5
161-170 | 15 | 0.5
171-180 | 6 | 10.5
181-190 | 5 | 19.5

The deviations are calculated by subtracting the median weight of 165.5 lbs from each weight category.

To find the absolute deviations, we take the absolute value of each deviation.

Weight (1b) | No.of persons | Deviation from Median | Absolute Deviation
----------- | ------------- | --------------------- | ------------------
131-140 | 3 | 34.5 | 34.5
141-150 | 8 | 24.5 | 24.5
151-160 | 13 | 14.5 | 14.5
161-170 | 15 | 0.5 | 0.5
171-180 | 6 | 10.5 | 10.5
181-190 | 5 | 19.5 | 19.5

To find the mean deviation, we need to find the average of the absolute deviations.

Mean Deviation = (34.5 + 24.5 + 14.5 + 0.5