Question 1155142
<font color=black size=3>
Let y be the missing number for now. 
The values in the probability P(X) row must add to 1
0.05+0.21+y+0.15+0.11 = 1
y+0.52 = 1
y = 1-0.52
y = 0.48
<font color=red>The missing number in the table is 0.48</font>



----------------------------------------------------------------------

Computing the mean (mu)


I'll write the table out like this
<table border = "1" cellpadding = "5">
<tr><td> X</td><td>P(X)</td></tr>
<tr><td>30</td><td>0.05</td></tr>
<tr><td>31</td><td>0.21</td></tr>
<tr><td>32</td><td>0.48</td></tr>
<tr><td>33</td><td>0.15</td></tr>
<tr><td>34</td><td>0.11</td></tr>
</table>



Now add on a X*P(X) column. Each row in this column is the result of multiplying the X and P(X) values for the given row. Eg: 31*0.21 = 6.51 for row 2
<table border = "1" cellpadding = "5">
<tr><td>X</td><td>P(X)</td><td>X*P(X)</td></tr>
<tr><td>30</td><td>0.05</td><td>1.5</td></tr>
<tr><td>31</td><td>0.21</td><td>6.51</td></tr>
<tr><td>32</td><td>0.48</td><td>15.36</td></tr>
<tr><td>33</td><td>0.15</td><td>4.95</td></tr>
<tr><td>34</td><td>0.11</td><td>3.74</td></tr>
</table>

Adding up everything in the X*P(X) column yields
1.5+6.51+15.36+4.95+3.74 = 32.06


<font color=red>The mean is mu = 32.06</font>


----------------------------------------------------------------------


Computing the standard deviation (sigma)


Subtract the mean mu = 32.06 from each data value X. This forms the (X-mu) column. 
Then square each value in that column to get another column (X-mu)^2
Finally, multiply that with the P(X) column


This is what the table should look like
<table border = "1" cellpadding = "5">
<tr><td>X</td><td>P(X)</td><td>X-mu</td><td>(X-mu)^2</td><td>(X-mu)^2*P(X)</td></tr>
<tr><td>30</td><td>0.05</td><td>-2.06</td><td>4.2436</td><td>0.21218</td></tr>
<tr><td>31</td><td>0.21</td><td>-1.06</td><td>1.1236</td><td>0.235956</td></tr>
<tr><td>32</td><td>0.48</td><td>-0.06</td><td>0.0036</td><td>0.001728</td></tr>
<tr><td>33</td><td>0.15</td><td>0.94</td><td>0.8836</td><td>0.13254</td></tr>
<tr><td>34</td><td>0.11</td><td>1.94</td><td>3.7636</td><td>0.413996</td></tr>
</table>

Add up the values in the last column

0.21218+0.235956+0.001728+0.13254+0.413996 = 0.9964


The variance is 0.9964


Take the square root of this to get sqrt(0.9964) = 0.9981984 approximately


<font color=red>sigma = 0.9981984 is the approximate standard deviation</font>
</font>