Problem 4E
The top 40 stocks on the overthecounter (OTC) market, ranked by percentage of outstanding shares traded on one day last year are as follows:
a Construct a relative frequency histogram to describe these data.
b What proportion of these top 40 stocks traded more than 4% of the outstanding shares?
c If one of the stocks is selected at random from the 40 for which the preceding data were taken, what is the probability that it will have traded fewer than5%of its outstanding shares?
Solution 4E
Step1 of 4:
Let us consider a random variable X it presents the top stocks on the over the counter market, ranked by percentage of outstanding shares traded on one day last year are as follows:
x  
11.8 
6.27 
5.49 
4.81 
4.4 
3.78 
3.44 
3.11 
2.88 
2.68 
7.99 
6.07 
5.26 
4.79 
4.05 
3.69 
3.36 
3.03 
2.74 
2.63 
7.15 
5.98 
5.07 
4.55 
3.94 
3.62 
3.26 
2.99 
2.74 
2.62 
7.13 
5.91 
4.94 
4.43 
3.93 
3.48 
3.2 
2.89 
2.69 
2.61 
Here our goal is:
a). We need to construct a relative frequency histogram to describe these data.
b). We need to find the proportion of these top 40 stocks traded more than 4% of the outstanding shares.
c). We need to find the probability that it will have traded fewer than 5% of its outstanding shares, when one of the stocks is selected at random from the 40 for which the preceding data were taken.
Step2 of 4:
a).
The given data can be rewrite in the form of Class interval
C.I. 
X(Midpoint) 
Frequency(f) 
Relative frequency 
2.613.93 
3.27 
20 
0.5 
3.935.25 
4.59 
10 
0.25 
5.256.57 
5.91 
6 
0.15 
6.577.89 
7.23 
2 
0.05 
7.899.21 
8.55 
1 
0.025 
9.2110.53 
9.87 
0 
0 
10.5311.85 
11.19 
0 
0 
11.8513.17 
12.51 
1 
0.025 


40 

Where,
1). Midpoint(X) can be calculated by using C.I. that is:
1