**Mean Deviation about Median**

Mean deviation about median is a measure of dispersion that quantifies the average absolute difference between the data values and the median of a distribution. It is calculated by taking the absolute differences between each data value and the median, summing them up, and dividing by the total number of data values.

To compute the coefficient of mean deviation about median, we need to divide the mean deviation about median by the median itself. The coefficient of mean deviation about median provides a standardized measure of dispersion relative to the median.

**Given Distribution:**

Waiting (kg) Number of Persons
40 - 50 8
50 - 60 12
60 - 70 20
70 - 80 10

**Step 1: Finding the Median**

To compute the median, we need to arrange the data values in ascending order and find the middle value. In this case, the data is already grouped, so we need to find the cumulative frequency.

Waiting (kg) Cumulative Frequency
40 - 50 8
50 - 60 8 + 12 = 20
60 - 70 20 + 20 = 40
70 - 80 40 + 10 = 50

The median is the value that corresponds to the cumulative frequency closest to (n/2), where n is the total number of data values. In this case, the total number of data values is 50, so (n/2) = 25. Therefore, the median falls in the 60-70 kg interval since the cumulative frequency of 40 is closest to 25.

**Step 2: Calculating the Mean Deviation about Median**

To calculate the mean deviation about median, we need to find the absolute differences between each data value and the median, sum them up, and divide by the total number of data values.

Waiting (kg) Absolute Difference (|x - Median|)
40 - 50 |60 - 45| = 15
50 - 60 |60 - 55| = 5
60 - 70 |60 - 65| = 5
70 - 80 |60 - 75| = 15

Sum of Absolute Differences = 15 + 5 + 5 + 15 = 40

Mean Deviation about Median = Sum of Absolute Differences / Total Number of Data Values = 40 / 50 = 0.8

**Step 3: Calculating the Coefficient of Mean Deviation about Median**

The coefficient of mean deviation about median is calculated by dividing the mean deviation about median by the median.

Coefficient of Mean Deviation about Median = Mean Deviation about Median / Median = 0.8 / 60 = 0.0133

Therefore, the coefficient of mean deviation about median for the given distribution is 0.0133 or 1.33%.

A random sample sample of size 28 is drawn from a nominal population .The summary statistics are x=68.6and s=1.28
1. construct a 95% confidence interval for the population meanµ