Corn plants from a test plot are measured, and the distribution of heights at 10-cm intervals is recorded in the following table:  

 Height (cm)      Plants (no.)       

100                    20       

110                    60       

120                    90       

130                   130       

140                   180      

 150                   120       

160                    70        

170                   50        

180                   40 

Calculate 

(a) the mean height, 

(b) the variance, 

(c) the standard deviation, and 

(d) the standard error of the mean. 

Plot a rough graph of plant height against frequency. Do the values represent a normal distribution? Based on your calculations, how would you assess the variation within this population?