Question
In: Statistics and Probability
Consider the grouped frequency distribution. Class Limits 3-5 6-8 9-11 12-14 15-17 f 4 10 10...
Consider the grouped frequency distribution.
| Class Limits | 3-5 | 6-8 | 9-11 | 12-14 | 15-17 |
| f | 4 | 10 | 10 | 5 | 10 |
(a) Find the mean. (Give your answer correct to two decimal places.)
(b) Find the variance. (Give your answer correct to two decimal
places.)
(c) Find the standard deviation. (Give your answer correct to two
decimal places.)
Solutions
Expert Solution
The following table shows the calculations-
|
Class limits |
Class Boundaries |
Frequency(fi) |
Mid-point of each class(xi) |
xi |
xi2 |
xi2 |
|
3-5 |
2.5-5.5 |
4 |
4 |
16 |
16 |
64 |
|
6-8 |
5.5-8.5 |
10 |
7 |
70 |
49 |
490 |
|
9-11 |
8.5-11.5 |
10 |
10 |
100 |
100 |
1000 |
|
12-14 |
11.5-14.5 |
5 |
13 |
65 |
169 |
845 |
|
15-17 |
14.5-17.5 |
10 |
16 |
160 |
256 |
2560 |
|
Total |
39 |
411 |
4959 |
fi
ANSWER a:
Mean= 10.54
ANSWER b:
Variance= 16.06
ANSWER c:
Standard Deviation= 4.01
(All the answers are correct upto 2 decimal places)
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