10+20/6 = Set A is 5?
and 500+20/6= Set B is 86.7 ? are those right? I did that without the formula because the formula confuses me.
The formula is not confusing. The problem is confusingly worded because it changes the definitions of the sets.
For set \(\displaystyle A = \{x_1,\ x_2,\ x_3,\ x_4,\ x_5\}.\)
\(\displaystyle \displaystyle \bar x_A = \dfrac{\displaystyle \sum_{i=1}^5x_i}{5} = 10 \implies\sum_{i=1}^5x_i = 5 * 10 = 50.\) Follow that?
Now let's define a new set \(\displaystyle H = \{x_1,\ x_2,\ x_3,\ x_4,\ x_5\, x_6\},\ where\ x_6 = 20.\)
So \(\displaystyle \displaystyle \bar x_H = \dfrac{\displaystyle \sum_{i=1}^6x_i}{6}.\) Still using the formula.
But what is the numerator in that formula equal to?
Here is the trick
\(\displaystyle \displaystyle \sum_{i=1}^6x_i = \left(\sum_{i=1}^5x_i\right) + x_6.\) Does that make sense?
And we know what the two terms on the right of the equation equal.
\(\displaystyle \displaystyle \sum_{i=1}^6x_i = 50 + 20 = 70 \implies \bar x_H = \dfrac{70}{6} \approx 11.67\)
Now try the second problem on your own, and let us know what you get.