wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The mean of 15 observations is 8. If the mean of the values of first eight observations is 7 and that of the values of last eight observations is 10, then what is the value of the 8th observation?


A
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
16
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
10
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 16
Let 15 observations be x1,x2,x3,,x15

Mean=Sum of values of all observationsNumber of observations

Sum of values of all observations = Mean x Number of observations
Sum of values of all observations = 15 × 8 = 120.
i.e.,
x1+x2+x3++ x15=120----(1)

Mean of first 8 observations = 7
Hence, the sum of first 8 observation = 7 × 8 = 56

x1+x2+x3++ x8=56----(2)

Mean of last 8 observations = 10
Hence, the sum of the last 8 observation = 10 ×8 = 80

x8+x9+x10++ x15=80-----(3)

Adding 2 and 3 we get,
(x1+x2+x3+,,+ x8)+(x8+x9+x10+,,+ x15)=56+80

x1+x2+x3++ x15+x8=136
substituting 1 in the above equation, we get,
120+x8=136

x8=136120 =16

Hence, the value of x8 is 16

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Mean
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon