Lakshya Education MCQs

Question: The mean of 15 observations is 8. If the mean of the first eight observations is 7 and that of the last eight observations is 10, then the value of the 8th observation is _____.
Options:
A.16
B.15
C.14
D.13
Answer: Option A
: A

We know that,
Mean = SumofallobservationsNumberofobservations

Sum of values of all the observations
=Mean×Numberofobservation
=15×8
=120

So, sum of thefirst eight observations
=Mean×Numberofobservation
=7×8
=56
Sum of the last eight observations
=Mean×Numberofobservation
=10×8
=80


Hence, value of the8thobservation
=(80+56)120
=16

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More Questions on This Topic :

Question 1. The mode of the given data 7, 9, 11, 13, 9 13, 9, 9, 7, 8 is 
___

: Mode is that value of the observation which occurs most frequently i.e. an observation with maximum frequency is called mode. In the above set of observations, '9' occurs most frequently and so it is the mode of the given data.
Question 2. The mean of the following distribution is

xi10131619fi2576
  1.    15.55
  2.    15.35
  3.    14.3
  4.    16
Answer: Option A
: A

Mean of ungrouped frequency distribution is given by ¯x=ni=1fixini=1fi
=(10×2+13×5+16×7+19×6)(2+5+7+6)
=31120

Therefore, themean of the data is 15.55.
Question 3. What is the median of the following data: 1, 4, 7, 3, 9, 5, 3, 2, 7, 5.
  1.    4
  2.    4.5
  3.    5
  4.    7
Answer: Option B
: B

For finding the median, the data should be arranged in ascending or descending order first.

Arranging the data in ascending order ,we get :
1, 2, 3, 3, 4, 5, 5, 7, 7, 9.

There are even number of observations.
Hence themedian is the mean value of (n2)th and [(n2)+1]th term.
Here the 102thterm= 5th term = 4
[(n2)+1]th term. = 6th term = 5
i.e. (4+52)=4.5
Hence, median of the given data =4.5
Question 4. Find the range of the following data: 26, 21, 33, 17, 14, 15, 27.
  1.    13
  2.    15
  3.    17
  4.    19
Answer: Option D
: D

The difference betweenthe highest and lowest values in the data is called the 'range' of the data. So, here the maximum value is 33 and the minimum is 14. So the difference between them i.e. 19 is the range of the given data.
Question 5. The graph below shows the ages of presidents of a country at the time of inauguration or start of their tenure. 



Find the correct option(s) among the following.
  1.    The total number of presidents is 45.
  2.    The youngest president was 44 years old
  3.    The youngest president was 39 years old.
  4.    The oldest president is 74 years old.
Answer: Option B
: B

On summing up all the frequencies, we get 4+11+14+9+4+2=44. Hence the total number of presidents is 44 and option A is incorrect. The graph starts from 39 but the corresponding frequency is 0. Hence, the age of 44 is the youngest age of president. Thus, B is correct and C is incorrect. The last point on thegraph having non-zero frequency is 69. 74 has zero frequency and hence option D is incorrect.

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