Question
Find the mean and standard deviation using short-cut method.
x_{i} |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
f_{i} |
2 |
1 |
12 |
29 |
25 |
12 |
10 |
4 |
5 |
Solution
The data is obtained in tabular form as follows.
x_{i} | f i | f_{i = `(X_i - 64)/1`} | y_{i}^{2} | f_{i}y_{i} | f_{i}y_{i}^{2} |
60 |
2 |
–4 |
16 |
–8 |
32 |
61 |
1 |
–3 |
9 |
–3 |
9 |
62 |
12 |
–2 |
4 |
–24 |
48 |
63 |
29 |
–1 |
1 |
–29 |
29 |
64 |
25 |
0 |
0 |
0 |
0 |
65 |
12 |
1 |
1 |
12 |
12 |
66 |
10 |
2 |
4 |
20 |
40 |
67 |
4 |
3 |
9 |
12 |
36 |
68 |
5 |
4 |
16 |
20 |
80 |
100 |
220 |
0 |
286 |
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Solution Find the Mean and Standard Deviation Using Short-cut Method.60 61 62 63 64 65 66 67 68 Concept: Variance and Standard Deviation - Shortcut Method to Find Variance and Standard Deviation.