Table of Contents

    Average

    Rumman Ansari July 28, 2024 427 views

    Average Formulas

    Average (Arithmetic Mean)

    The average or arithmetic mean of a set of numbers is the sum of the numbers divided by the count of the numbers.

    \[ \text{Average} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \]

    Weighted Average

    The weighted average is calculated by multiplying each observation by its respective weight, summing these products, and then dividing by the total sum of the weights.

    \[ \text{Weighted Average} = \frac{\sum (w_i \times x_i)}{\sum w_i} \]

    Average Speed

    The average speed is the total distance traveled divided by the total time taken.

    \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

    Harmonic Mean

    The harmonic mean of a set of numbers is the number of observations divided by the sum of the reciprocals of the observations.

    \[ \text{Harmonic Mean} = \frac{n}{\sum \frac{1}{x_i}} \]

    Geometric Mean

    The geometric mean of a set of numbers is the nth root of the product of the numbers, where n is the number of observations.

    \[ \text{Geometric Mean} = \left( \prod_{i=1}^n x_i \right)^{\frac{1}{n}} \]
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    MCQ Section

    MCQ 1
    The average of the first nine prime numbers is
    MCQ 2
    What is the mean of all prime numbers that are within the range of 30 and 50, inclusive?
    MCQ 3
    What is the mean of the first 40 natural numbers?
    MCQ 4
    What is the mean weight of the entire class, given that section A has 36 students with an average weight of 40kg and section B has 44 students with an average weight of 35kg?
    MCQ 5
    How much money did the group of nine people spend in total at the hotel, given that eight of them spent Rs.12 each on their meals and the ninth person spent Rs.8 more than the average expenditure of all nine people?
    MCQ 6
    What is the largest of the three numbers, given that the second number is twice the first and is also thrice the third, and that the average of the three numbers is 44?
    MCQ 7
    What is the sixth result when given the average of the first six results is 58, the average of the last six results is 63, and the average of all 11 results is 60?
    MCQ 8
    Find the weight of B given that the average weight of A, B, and C is 45 kg, the average weight of A and B is 40 kg, and the average weight of B and C is 43 kg.
    MCQ 9
    Find the weight of the new man given that the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew members, who weighs 53 kg, is replaced by the new man.
    MCQ 10
    Find the average score of the batsman after the 17th inning given that he made 87 runs in that inning and it increased his average by 3.
    MCQ 11
    What is the 13th result, given that the average of 25 results is 18, the average of the first 12 results is 14, and the average of the last 12 results is 17?
    MCQ 12
    Find the age of the teacher given that the average age of a class of 39 students is 15 years and the average increases by 3 months when the teacher's age is included.
    MCQ 13
    What is the mean of the first five multiples of 12?
    MCQ 14
    If the average of five numbers is 20 and each number is multiplied by 2, what will the average of the resulting numbers be?
    MCQ 15
    What is the largest of three consecutive even numbers if their average is 34?
    MCQ 16
    If the average of Sohan's marks in six subjects is 74 and his average in five subjects excluding science is 70, how many marks did he get in science?
    MCQ 17
    The average age of a group of 30 boys is 16 years, and a boy of age 19 leaves the group. A new boy joins the group, and the average age of the group becomes 15.8 years. What is the age of the new boy?
    MCQ 18
    The average age of 30 boys in a class is 15 years. When the ages of two teachers are included, the average age increases by 1. What is the sum of the ages of the two teachers?
    MCQ 19
    Four years ago, the average age of A and B was 20 years. Today, the average age of A, B, and C is 25 years. What will be the age of C after 7 years?
    MCQ 20
    The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them, whose weight is 65 kg. What is the weight of the new woman?
    MCQ 21
    The average weight of 10 men is decreased by 2 kg when one of them, whose weight is 60 kg, is replaced by a new man. What is the weight of the new man?
    MCQ 22
    The captain of a cricket team of 11 members is 26 years old, and the wicket-keeper is three years older than the captain. If the ages of the captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?
    MCQ 23
    The average monthly income of Rakesh and Suresh is Rs. 5050, the average monthly income of Suresh and Ramesh is Rs. 6250, and the average monthly income of Rakesh and Ramesh is Rs. 5200. What is the monthly income of Rakesh?
    MCQ 24
    According to Varun, his weight is greater than 65 kg but less than 72 kg. His father believes that Varun's weight is greater than 60 kg but less than 70 kg, and his sister thinks that his weight cannot be greater than 68 kg. If all of these estimations are correct, what is the average of the different possible weights of Varun?
    MCQ 25
    The average weight of P, Q, and R is 45 kg. The average weight of P and Q is 40 kg, and the average weight of Q and R is 43 kg. What is the weight of Q?
    MCQ 26
    The average weight of 16 students in a class is 50.25 kg, and the average weight of the remaining 8 students is 45.15 kg. What is the average weight of all the students in the class?
    MCQ 27
    In a class, the average age of 15 boys is 11. If 5 boys each of age 9 years are added, what will be the new average?
    MCQ 28
    What is the average of the squares of the first 6 consecutive even numbers?
    MCQ 29
    What is the average of the first 4 consecutive even numbers?
    MCQ 30
    A museum has an average of 510 visitors on Sunday and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
    MCQ 31
    The average marks of three classes of 45, 60, and 55 students are 60, 55, and 50, respectively. What is the average marks of all the students?
    MCQ 32
    The number of quantities in group A is 10, and the number of quantities in group B is 8. The individual average of group A is 24, and the individual average of group B is 16. What is the combined average of the two groups?
    MCQ 33
    What is the average of the first 5 consecutive even numbers starting from 2 to 10, where the last even number is 10?
    MCQ 34
    What is the average of the squares of the first 6 consecutive even numbers starting from 2 to 12, where the last even number is 12?
    MCQ 35
    What is the sixth number if the average of 11 numbers is 30, the average of the first six numbers is 17.5, and the average of the last six numbers is 42.5?
    MCQ 36
    The average of the first 100 positive integers is __
    MCQ 37
    The average of two numbers is xy.If one number is X the other is
    MCQ 38
    The average of marks of 13 papers is 40.The average of the first 7 papers is 42 and that of the last 7 papers is 35 .What are the marks of the seventh paper?
    MCQ 39
    What is the middle number if the average of 15 numbers is 15, the average of the first five numbers is 14, and the average of the other 9 numbers is 16?
    MCQ 40
    Which is the largest number if the average of four consecutive even numbers is 27?
    MCQ 41
    2 years ago, the average age of a family of 5 members was 16 years. After a baby is born, the average age of family is the same today. Find the present age of the baby.
    MCQ 42
    , John's marks were wrongly entered as 83 instead of 63. If the average marks calculated for the whole class increased by half, then find the number of students in the class
    MCQ 43
    What is the corrected mean of 40 observations, given an initial mean of 46, when it is discovered that one of the observations, which was recorded as 33, should have been recorded as 38?
    MCQ 44
    The average salary of workers of a factory is RS6000,while the average salary of technicians is RS12000 and that of non-technicians is RS3750.Find the total number of workers in the factory?
    MCQ 45
    The average score of girls in class X examination in a school is 73 and that of boys is 71.The average score in class X of that school is 71.8.Find the percentage of the number of girls and boys in class X of the school?
    MCQ 46
    The average of odd numbers upto 100 is___
    MCQ 47
    In a class there are 50 students.Their average weight is 45kg.When a student leaves the class ,the average is reduced by 100g.Find the weight of the student who left?
    MCQ 48
    The average of five numbers is 58.Yhr average of the first two numbers is 48.5 and the average of last two numbers is 53.5.What is the third number?
    MCQ 49
    Six person went to a hotel for taking their meals.Five of them spent rs.32 each on their meals while the sixth person spent rs.80 more than the average expenditure of all the six.What was the total money spent by all?
    MCQ 50
    13 chairs and 5 tables were bought for rs 8280.If the average cost of a table be rs.1227.What is the average cost of a chair?
    MCQ 51
    The average age of a man and his son is 40 years.The ratio of their ages is 11:5 respectively.What is the son's age?
    MCQ 52
    Of the three numbers ,second is twice the first and is also thrice the third.If the average of three numbers is 44,what is the largest number?
    MCQ 53
    A batsman makes a score of 87 runs in the 17th innings and thus increases his average by 3.Find his average after 17 innings?
    MCQ 54
    The average of 11 players of a cricket team is increased by 2 months when two of them aged 18 years and 20 years are replaced by two new players.Find the average age of the new players?
    MCQ 55
    10 years ago the average age of a family of 4 members was 24 years.Since then,two children having been born , still the average age of the family is the same today If the two children differ in age by 2 years,find the present age of the younger child?
    MCQ 56
    Find the average of all prime numbers between 30 and 50
    MCQ 57
    The body weight of six boys is recorded as 54kg,64kg,75kg,67kg,45kg and 91kg.What is the average body weight of all six boys?