91Ó°ÊÓ

A histogram of the monthly return distribution for the US stock market over a 273-month period.

Because the highest bars in the histogram are to the right, with a tail of smaller bars to the left, the distribution is skewed to the left.

The distribution appears to have three outliers because there are two bars (one with frequency 2 and one with frequency 1) that are separated from the other bars of the histogram by a gap.

The gaps are roughly at -20 and -13, with two potential outliers between -25 and -22.5 and one other between -17.5 and -15.

As a result:

Skewed to the left

2 gaps

3 Potential outlier

We anticipate that the distribution's center will be near the top of the histogram.

Because the highest bar has monthly percent returns ranging from 0% to 2.50%, we estimate the center of this distribution to be between 0% and 2.50%.

As a result:

To be between 0 and 2.5 percent

The leftmost bar in the histogram represents the lowest return.

We cannot, however, determine the exact value of the minimum return because we have not been given its exact value and only know a range of possible values for the minimum return from the corresponding bar in the histogram.

The leftmost bar in the histogram represents monthly percent returns on common stocks ranging from -25 to -22.5 percent, implying that the minimum return is between -25 and -22.5 percent.

A s a result:

We can't figure out the exact value of the minimum return because we haven't been given it, and we only know a range of possible values for the minimum return from the corresponding bar in the histogram.

The minimum return ranges between -25 and -22.5 percent.

Let us first estimate the frequency of each bar's interval, which is given by the height of the bar.

Add the frequencies of all intervals with negative returns next.

$2+0+0+1+0+4+6+11+28+50=102$

As a result, we can see that 102 of the 273 months in the sample have a return less than zero.

$$\begin{gathered} \frac{102}{273}=\frac{34}{91} \\ \frac{34}{91}≈0.3736 \\ 0.3736=37.36\% \end{gathered}$$

This means that 37.36 percent of the three months had returns less than zero.