Table below shows the frequency f with which 'x' alpha particles were radiated from a diskette
x :  0  1  2  3  4  5  6  7  8  9  10  11  12 
f :  51  203  383  525  532  408  273  139  43  27  10  4  2 
Calculate the mean and variance.
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Solution
Mean,
\[\bar{X} = \frac{\sum f_i x_i}{\sum f_i} = \frac{10078}{2600} = 3 . 88\]
\[x_i\]

\[f_i\]

\[f_i x_i\]

\[x_i  \bar{X}\]

\[\left( x_i  \bar{X} \right)^2\]

\[f_i \left( x_i  \bar{X} \right)^2\]

0  51  0  −3.88  15.05  767.55 
1  203  203  −2.88  8.29  1682.87 
2  383  766  −1.88  3.53  1351.99 
3  525  1575  −0.88  0.77  404.25 
4  532  2128  0.12  0.014  7.448 
5  408  2040  1.12  1.25  510 
6  273  1638  2.12  4.49  1225.77 
7  139  973  3.12  9.73  1352.47 
8  43  344  4.12  16.97  729.71 
9  27  243  5.12  26.21  707.67 
10  10  100  6.12  37.45  374.5 
11  4  44  7.12  50.69  202.76 
12  2  24  8.12  65.93  131.86 
\[\sum f_i = N = 2600\]

\[\sum f_i x_i = 10078\]

\[\sum f_i \left( x_i  \bar{X} \right)^2 = 9448 . 848\]

Variance,
\[\sigma^2 = \frac{\sum f_i \left( x_i  \bar{X} \right)^2}{N} = \frac{9448 . 848}{2600} = 3 . 63\]
Is there an error in this question or solution?
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