Final answer:
To find the mean and standard deviation, you sum the marks and divide by the number of students, then calculate the variance and square root for the standard deviation. Adding 4 to every mark will increase the mean but the standard deviation will remain unchanged because it measures the spread of numbers, not their starting value.
Step-by-step explanation:
To find the mean of the marks obtained by 10 students, we first sum the marks and then divide by the number of students. The original marks are: 42, 48, 47, 43, 45, 49, 48, 41, 46, 41. We calculate the mean (average) as follows:
- Add all the marks together: 42 + 48 + 47 + 43 + 45 + 49 + 48 + 41 + 46 + 41 = 450.
- Divide the total by the number of marks (10 students): 450 / 10 = 45.
The mean score is 45.
To find the standard deviation, we follow these steps:
- Subtract the mean from each mark and square the result: (42-45)^2, (48-45)^2, etc.
- Sum these squared differences.
- Divide by the number of marks minus one to find the variance (because this is a sample, not a population).
- Take the square root of the variance to get the standard deviation.
If every mark is increased by 4, this will increase the mean, but the standard deviation will remain the same. The standard deviation is a measure of how spread out numbers are, and adding a constant to every number does not change the spread.