Statistics And Probability Question 427
Question: What is the standard deviation of the following series |Measurements|0-10|10-20|20-30|30-40|
[DCE 1996]
|—|—|—|—|—| |Frequency|1|3|4|2|
Options:
A) 81
B) 7.6
C) 9
D) 2.26
Show Answer
Answer:
Correct Answer: C
Solution:
| Class | fiyi | $d=y_{i}-A$ | , | A=25 | fidi | fidi2 |
|---|---|---|---|---|---|---|
| 0-10 | 1 | 5 | ? | 20 | ? | 20 |
| 10-20 | 3 | 15 | ? | 10 | ? | 30 |
| 20-30 | 4 | 25 | 0 | 0 | 0 | |
| 30-40 | 2 | 35 | 10 | 20 | 200 | |
| Total | 10 | ? | 30 | 900 |
$ {{\sigma }^{2}}=\frac{\sum f_{i}d_i^{2}}{\sum f_{i}}-{{( \frac{\sum f_{i}d_{i}}{\sum f_{i}} )}^{2}}=\frac{900}{10}-{{( \frac{-30}{10} )}^{2}} $ $ {{\sigma }^{2}}=90-9=81 $ Þ s = 9.
BETA
