Question

The mean of 10 observation is 7 and the mean of 15 observation is 2 then the mean of all observations is

Answer 1

mean = sum of observation /no. of observation
mean of 10 observation is 7
sum of 10 observation = 7*10 = 70
mean of 15 observation is 2
sum of 15 observation = 15*10
so we want to find mean of all 25 observation
= sum of 10 observation +sum of 15 observation/25

= 7*10+15*2/25 = 100/25 = 4

Answer 2

Hi.

Here is your answer---

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In First Case,

Mean of 10 observations(∑1) = 7
Number of Observations(n1) = 10

Using the Formula,
                        ∑ = ∑x1 ÷ n1
                     ∑x1= ∑1 × n1
                            =  7 × 10
                            = 70

In second Case,

                                  Mean(∑2) = 2
 Number of observations(n2) = 15

Again,
          ∑x2 = ∑2 × n2
               =  2 × 15
               = 30

For total Mean,
    Total Number of Observations(n) = n1 + n2
                                                    = 10 + 15
                                                     = 25

Total Sum of all observations(∑x) = ∑x1 + ∑x2
                                                      =  70 + 30
                                                      = 100

Using the Formula,
       Mean(∑) = Sum of all observations(∑x) ÷ Number of Observations(n)
                      = 100/25
                      = 4

Thus, the Final Mean of all observations is 4.

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Hope it helps.

Have a nice day.