The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway: Speed (miles per Hour) | 50-54 | 55-59 | 60-64 | 65-69 | 70-74 | 75-79 Frequency | 2 | 4 | 5 | 10 | 9 | 5 Calculate the; a) Median speed. b) Mean speed using assumed method. c) Standard deviation. d) Karlpearsons coefficient of skewness and comment on the distribution of the speed of the automobiles.

Here is the solution for the given frequency distribution:

First, we prepare the data by finding the class boundaries, midpoints, and cumulative frequencies. The class width $c = 5$.

| Speed (miles per Hour) | Frequency ($f$) | Class Boundaries | Midpoint ($x$) | Cumulative Frequency (cf) | |:-----------------------|:----------------|:-----------------|:---------------|:--------------------------| | 50-54 | 2 | 49.5 - 54.5 | 52 | 2 | | 55-59 | 4 | 54.5 - 59.5 | 57 | 6 | | 60-64 | 5 | 59.5 - 64.5 | 62 | 11 | | 65-69 | 10 | 64.5 - 69.5 | 67 | 21 | | 70-74 | 9 | 69.5 - 74.5 | 72 | 30 | |