16000 students appeared in TY BCom examination the ratio of number of ...
**Given Information:**
- Total number of students appeared in TY BCom examination = 16000
- Ratio of number of boys to girls = 3:5
- Number of passed students exceeds the number of failed students by 8000
- Number of girls failing in the examination = 2400
**To Find:**
- Coefficient of association between student and success
**Solution:**
**Step 1: Calculate the number of boys and girls**
Let the number of boys be 3x and the number of girls be 5x. According to the given ratio,
3x + 5x = 16000
8x = 16000
x = 2000
So, the number of boys = 3 * 2000 = 6000
And the number of girls = 5 * 2000 = 10000
**Step 2: Calculate the number of passed and failed students**
Let the number of passed students be P and the number of failed students be F. According to the given information,
P - F = 8000 ...(1)
Also, the total number of students is equal to the sum of passed and failed students,
P + F = 16000 ...(2)
By solving equations (1) and (2), we get
2P = 24000
P = 12000
Substituting the value of P in equation (2), we get
12000 + F = 16000
F = 4000
So, the number of passed students = 12000 and the number of failed students = 4000
**Step 3: Calculate the number of girls failing**
Given that the number of girls failing in the examination = 2400
So, the number of boys failing = 4000 - 2400 = 1600
**Step 4: Calculate the coefficient of association**
The coefficient of association between two attributes is given by the formula:
Coefficient of Association = (Number of students with both attributes - Expected value) / sqrt(Expected value)
Here, the two attributes are "student" and "success".
Number of students with both attributes = Number of passed students = 12000
Expected value = (Total number of students / Total number of attributes) * (Total number of attributes with the first attribute / Total number of students)
Expected value = (16000 / 2) * (12000 / 16000)
Expected value = 6000
Substituting the values in the formula, we get
Coefficient of Association = (12000 - 6000) / sqrt(6000)
Coefficient of Association = 6000 / sqrt(6000)
Using a calculator, we find that the coefficient of association is approximately 43.30.
Therefore, the coefficient of association between student and success is approximately 43.30.
16000 students appeared in TY BCom examination the ratio of number of ...
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