1.2 The average of 22 numbers is 37.5. The average of first 12 numbers is 40.6 and that of the last 12 numbers is 35 4 1 11th and 12th numbers are excluded, then what is the average of the remaining mumbers?
Answers
Answer:
Average is the sum of the data values divided by the total number of data values.
Let the 11 numbers be x
1
,x
2
,x
3
,x
4
,x
5
,x
6
,x
7
,x
8
,x
9
,x
10
,x
11
Given that average of first 6 numbers is 34
⟹34=
6
x
1
+x
2
+x
3
+x
4
+x
5
+x
6
⟹x
1
+x
2
+x
3
+x
4
+x
5
+x
6
=34×6=204 ------(1)
Given that average of last 6 numbers is 33
⟹33=
6
x
6
+x
7
+x
8
+x
9
+x
10
+x
11
⟹x
6
+x
7
+x
8
+x
9
+x
10
+x
11
=33×6=198
⟹x
7
+x
8
+x
9
+x
10
+x
11
=198−x
6
------(2)
Given that average of all the 11 numbers is 32
⟹32=
11
x
1
+x
2
+x
3
+x
4
+x
5
+x
6
+x
7
+x
8
+x
9
+x
10
+x
11
------(3)
substituting (1) and (2) in (3) we get
32=
11
204+198−x
6
⟹402−x
6
=352
⟹x
6
=402−352=50
Therefore, the sixth number is 50
Step-by-step explanation:
hope it will help.
Given,
Average of 22 numbers
Average of first 12 numbers
Average of last 12 numbers
Solution,
Sum of 22 numbers,
Sum of first 12 numbers,
Sum of last 12 numbers,
11th and 12th number is excluded.
Then sum of first 10 numbers.
The sum of last 10 numbers.
Calculate the average of remaining numbers.
Hence the average of remaining numbers is