Question

A group of 20 values has a mean of 85 and a median of 80. A different
group of 30 values has a mean of 75 and a median of 72.
(a) What is the mean of the 50 values?
(b) What is the median of the 50 values?​

Answer 1

Answer:

(a) 79  (b) Insufficient data

Step-by-step explanation:

(a) let X represent the first group of values; X = {$x_1, x_2, x_3,..., x_{20}$}

and Y = {$y_{1}, y_{2}, y_{3},..., y_{30}$}

given: η(X) = 85 and η(Y) = 75

η of 50 values = η(X + Y)

η(X + Y) = $\frac{1}{50} [X_{1,2,3...20} + Y_{1,2,3,..., 30}]$

$X_{1,2,3,...,20} = 85 * 20 = 1700\\Y_{1,2,3,..., 30} = 75*30 = 2250$

Hence, η(X + Y) = $\frac{1}{50}[1700 + 2250]$

                          = 79

(b) to find the median of a group of values, we need the values itself.