The return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. The figure above is a histogram of the distribution of the monthly returns for all stocks listed on the U$.$S$.$ markets from January $1985$ to November $2010(311$ months$).$ The extreme low outlier is the market crash of October $1987,$ when stocks lost $23\%$ of their value in one month. The other two outliers are $16\%$ during August $1998,$ a month when the Dow Jones Industrial Average experienced its second largest drop in history to that time, and the financial crisis in October $2008$ when stocks lost $17\%$ of their value.

$($a$)$ Describe the overall shape of the distribution of the monthly returns. $[3]$

$($b$)$ What is the approximate center of this distribution? $[2]$

$($c$)$ Approximately what were the smallest and largest monthly returns, leaving out the outliers? $[2]$

$($d$)$ A return less than zero means that stocks lost value in that month. About what

percent of all months had returns less than zero. $[3]$