Answer:
The mean of 25 students is 17.6
Step-by-step explanation:
The formula of the mean (average) is mean (average) =
, where S is the sum of the data, and N is the number of the data
∵ The average marks of the first 10 students are 17
- That means the mean is 17 and the number of students is 10
∴ Average = 17
∴ N = 10
∵ Average =
- Substitute average by 17 and N by 10
∴ 17 = ![\frac{S}{10}](https://tex.z-dn.net/?f=%5Cfrac%7BS%7D%7B10%7D)
- Multiply both sides by 10
∴ 170 = S
∴ The sum of the marks of the first 10 students is 170
∵ The average of the next 15 students is 18
∴ Average = 18
∴ N = 15
- Substitute average by 18 and N by 15
∴ 18 = ![\frac{S}{15}](https://tex.z-dn.net/?f=%5Cfrac%7BS%7D%7B15%7D)
- Multiply both sides by 15
∴ 270 = S
∴ The sum of the marks of the next 15 students is 270
Now to find the mean of 25 students and the two sums and divide the answer by 25
∵ S = 170 + 270
∴ S = 440
∵ N = 25
∴ Mean = ![\frac{440}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B440%7D%7B25%7D)
∴ Mean = 17.6
The mean of 25 students is 17.6