Question

Complete these two different sets of data so that they each have six values and a mean of 21 . 20,20.5,20.5,21.5,21.5, 20,21,21,21,21

Answer 1

Answer:

The complete first set is;

20, 20.5, 20.5, 21.5, 21.5, 22

The complete second set is;

20, 21, 21, 21, 21, 22

Step-by-step explanation:

The mean or the average value of a data set is simply;

(sum of the values in the data set) / ( number of values in the set)

In the first set we are given the following values;

20,20.5,20.5,21.5,21.5

We are required to complete this set so that we have a total of 6 values with a mean of 21.

We let the sixth value be x. Going by the above definition of the mean we have the following equation;

$21=\frac{20+20.5+20.5+21.5+21.5+x}{6}$

We simplify the equation and solve for x;

$21=\frac{104+x}{6}\\126=104+x\\x=126-104\\x=22$

The complete set is thus;

20,20.5,20.5,21.5,21.5,22

In the second set we are given the following values;

20,21,21,21,21

We are also required to complete this set so that we have a total of 6 values with a mean of 21.

We let the sixth value be y. Going by the above definition of the mean we have the following equation;

$21=\frac{20+21+21+21+21+y}{6}$

We simplify the equation and solve for y;

$21=\frac{104+y}{6}\\126=104+y\\y=126-104\\y=22$

The complete set is thus;

20,21,21,21,21,22