Lakshya Education MCQs

Question: Median is defined as:
Options:
A.the data which is the largest in a data set.    
B.the data which lies in the middle of an organised data set.
C. same as mean.  
D.the observation that occurs most frequently.    
Answer: Option B
: B

Median is defined as the data which lies in the middle of an organised data set. Median refers to the value which lies in the middle of the data (when arranged in an increasing or decreasing order) with half of the observations above it and the other half below it.

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Question 1. There are 50 students in a class and the average mark scored by the class in Maths is 65 out of 100. The total marks scored by all the students except Karan and Arjun is 3080. If the marks scored by Karan & Arjun are same. What is the mark scored by Arjun?
  1.    75
  2.    80
  3.    85
  4.    90
Answer: Option C
: C

Average =Total marksTotal number of student 65=3080+Marks scoredbyArjun+Marksscored by Karan50. Since marks scored by Arjun =Marks scored by Karan Marks scored by Arjun +Marks scored by Karan =2 × Marks scored by Arjun. So, 65 × 50 = 3080 + 2 × Marks scored by Arjun. So, marks scored by Arjun =325030802=1702=85 marks.
Question 2. In the game of ludo, you start your move if you get 6 after throwing the dice for the first time. What is the probability that you will start your move after the first throw?
  1.    13
  2.    14
  3.    15
  4.    16
Answer: Option D
: D

The probability of getting digit '6' (from the digits 1,2,3,4,5,6) after throwing the dice for the first time
=Number of favourable outcomesTotal number of outcomes=16

Here the total number of outcomes is 6 and the number of favourable outcomes is 1 as the value of '6' is there for one time.
Question 3. Which of the following is always equal to one of the observations in the data set?
  1.    Median
  2.    Mode   
  3.    Both median & mode
  4.    Mean 
Answer: Option B
: B

Mean and Range may or may not be equal to any of the observations from the data set. Median is one of the observations if the number of observations is odd. If it's even, median also won't be equal to one of the observations. But mode is always equal to one of the observations.
Question 4. Find the difference between the median and the mode of the following data set:

1          6          45        4          33        12        19        6          56        25        13        9
  1.    12.5
  2.    12
  3.    6.5
  4.    6
Answer: Option C
: C

Arranged data set is: 1 4 6 6 9 12 13 19 25 33 45 56

Median: The middle most value after arranging the given data.

Here, the number of observations is 12, which is an even number.So, we take the average of thetwo observations in the middle to find the value of median. Median=12+132=12.5. (Mean of the 6th and7th observation)

Mode:Theobservation that occurs most often in the data set.

We can find 6 two times in the data set. This is the most repeated value in the data set. The value of the mode is 6.

i.e., Mode=6.
Difference betweenmedian and mode of the given data set=12.5-6=6.5.
Question 5. There is a data set with 1000 observations. Out of these observations, the observation that occurs most frequently is 9, which occurs 13 times. After taking 20 more observations, it was observed that 13, which was not there in the observations before, occurred 19 out of 20 times and 9 occurred only 1 out of 20 times. What is the mode in these 1020 observations?


___

: In the 1000 observations, 9 will be the mode. In 1020 observations, frequency of 9 = 13 + 1 = 14 In 1020 observations, frequency of 13 = 19 So, mode of the observations = 13.
Question 6. If the X- axis represents various fruits purchased and the Y-axis represents sales(in kgs), then match the following.

 
  1.    1-a , 2-b  , 3-d , 4-c , 5-e   
  2.    1-c  , 2-d , 3-b , 4-e , 5-a    
  3.    1-d , 2-c , 3-a , 4-b , 5-e   
  4.    1-b , 2-c , 3-e , 4-a , 5-d    
Answer: Option B
: B

As seen from the graph,
the quantity of apples sold = 5 kg,
the quantity of mangoessold= 15 kg,
the quantity of bananas sold = 20 kg,
the quantity of pineapples sold = 10 kg and
the quantity of papayas sold = 25 kg.
Thus, 1 - c,2 - d,3 - b,4 - e,5 - a is correct.

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