Question

The average marks of the first 10 students are 17 and that of the next 15 students is 18. find the mean of 25 students?

can u give the explanation pls like step by step

Answer 1

The mean of 25 students is 17.6

Explanation:

The formula of the mean (average) is mean (average) =
`(S)/(N)` , 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 =
`(S)/(N)`

- Substitute average by 17 and N by 10

∴ 17 =
`(S)/(10)`

- 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 =
`(S)/(15)`

- 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 =
`(440)/(25)`

∴ Mean = 17.6

The mean of 25 students is 17.6