Question

if the mean of five observations z,z+2,z+4,z+6,z+8 is 11, then the mean of the last three observations is what

Answer 1

Answer:

The mean of last three observations is 13

Step-by-step explanation:

Given :

The mean of five observations z, z+2 ,z+4, z+6, z+8 is 11

To find :

the mean of the last three observations

Solution :

We know,

$\boxed{\rm Mean=\dfrac{sum \ of \ observations}{no.of \ observations}}$

First, let's find the value of z.

Number of observations = 5

Mean = 11

$\tt 11=\dfrac{z+z+2+z+4+z+6+z+8}{5} \\\\ \tt 11 \times 5 =5z+20 \\\\ \tt 55=5z+20 \\\\ \tt 5z=55-20 \\\\ \tt 5z=35 \\\\ \tt z=35/5 \\\\ \tt z=7$

Now, the last three observations are

• z+4 = 7 + 4 = 11
• z+6 = 7 + 6 = 13
• z+8 = 7 + 8 = 15

Number of observations = 3

Mean = ?

$\sf Mean=\dfrac{11+13+15}{3} \\\\ \sf Mean=\dfrac{39}{3} \\\\ \sf Mean=13$

Therefore, the mean of last three observations is 13