# Averages : Arithmetic Mean, Median, Mode

The averages and statistics topic tests concepts that include average, weighted average, median, mode, standard deviation and range. You are likely to find a question that tests standard deviation in XAT than in TANCET. If you are a TANCET aspirant, you could restrict yourself to all questions other than the ones on Standard Deviation. The practice questions given below have detailed explanations, video explanations in some cases and have been classified on the basis of the concept tested in the question. The level of difficulty of the question is also marked to help you gauge the question.

The average monthly salary of 12 workers and 3 managers in a factory was 600. When one of the managers whose salary was 720, was replaced with a new manager, the average salary of the team went down to 580. What is the salary of the new manager?

- 570
- 420
- 690
- 640
- 610

**Correct Answer**Choice (2). 420 Correct answer- Explanatory answer
- New average after replacement
- Medium

The average wage of a worker during a fortnight comprising 15 consecutive working days was 90 per day. During the first 7 days, his average wage was 87/day and the average wage during the last 7 days was 92/day. What was his wage on the 8th day?

- 83
- 92
- 90
- 97
- 96

**Correct Answer**Choice (4). 97 Correct answer- Explanatory answer
- Finding one term : given averages
- Medium

The average of 5 quantities is 6. The average of 3 of those 5 quantities is 8. What is the average of the remaining two quantities?

- 6.5
- 4
- 3
- 3.5
- 4.2

The average temperature on Wednesday, Thursday and Friday was 25

^{o}. The average temperature on Thursday, Friday and Saturday was 24^{o}. If the temperature on Saturday was 27^{o}, what was the temperature on Wednesday?- 24
^{o} - 21
^{o} - 27
^{o} - 30
^{o}

- 24
The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is ____

- 24
- 26
- 28
- 22

**Correct Answer**Choice (1). 24 Correct answer- Explanatory answer
- Computing New average
- Easy

When a student weighing 45 kg left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

- 57 kg
- 56.8 kg
- 58.2 kg
- 52.2 kg

**Correct Answer**Choice (1). The average weight of the remaining 59 students is 57 kg Correct answer- Explanatory answer
- Average after a student leaves
- Easy

Three math classes: X, Y, and Z, take an algebra test.

The average score in class X is 83.

The average score in class Y is 76.

The average score in class Z is 85.

The average score of all students in classes X and Y together is 79.

The average score of all students in classes Y and Z together is 81.

What is the average score for all the three classes, taken together?- 81
- 81.5
- 82
- 84.5

The average weight of a class of 24 students is 36 kg. When the weight of the teacher is also included, the average weight increases by 1 kg. What is the weight of the teacher?

- 60 kg
- 61 kg
- 37 kg
- None of the above

**Correct Answer**Choice (2).

The weight of the teacher is 61 kg. Correct answer- Explanatory answer
- New Average after adding a person
- Easy

The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?

- 11
- 12
- 11.5
- 12.5

The average age of a family of 5 members is 20 years. If the age of the youngest member is 10 years, what was the average age of the family just a day before the birth of the youngest member?

- 13.5
- 14
- 15
- 12.5
- 10

**Correct Answer**Choice (4).

The average age of the family just a day before the birth of the youngest member is 12.5 years. Correct answer- Explanatory answer
- Average at two different points in time
- Medium

A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b?

- 8
- 6
- 2
- 4
- 18

**Correct Answer**Choice (3).

The difference between the digits of the two-digit number is 2. Correct answer- Explanatory answer
- Finding digits of a two-digit number
- Medium

Average cost of 5 apples and 4 mangoes is 36. The average cost of 7 apples and 8 mangoes is 48. What is the total cost of 24 apples and 24 mangoes?

- 1044
- 2088
- 720
- 324

**Correct Answer**Choice (2).

The cost of 24 apples and 24 mangoes is 2088. Correct answer- Explanatory answer
- Linear equations in averages
- Easy

Average weight of 25 boys in a class is 48 kg. The average weight of class of 40 students is 45 kg. What is the average weight of the 15 girls in the class?

- 44 kg
- 42 kg
- 40 kg
- 39 kg
- 42.5 kg

**Correct Answer**Choice (3).

The average weight of the 15 girls is 40 kg. Correct answer- Explanatory answer
- Finding average of a subset
- Medium

Ramesh analysed the monthly salary figures of five vice presidents of his company. All the salary figures are in integer lakhs. The mean and the median salary figures are 5 lakhs, and the only mode is 8 lakhs. Which of the options below is the sum (in lakhs) of the highest and the lowest salaries?

- 9
- 10
- 11
- 12
- None of the above

A class had 9 students. In one test, the class average was 61. One student's paper was scored incorrectly, and the resulting score was raised 18 points. What is the corrected class average?

- 70
- 63
- 72
- 78
- 74

## XAT TANCET Practice Questions - Listed Topic wise

- Number Theory
- Permutation Combination
- Probability
- Inequalities
- Geometry
- Coordinate Geometry
- Mensuration
- Trigonometry
- Data Sufficiency
- Percentages
- Profit Loss
- Ratio Proportion
- Mixtures & Alligation
- Speed Distance & Time
- Pipes, Cisterns & Work, Time
- Simple & Compound Interest
- Races
- Averages & Statistics
- Progressions : AP, GP & HP
- Set Theory
- Clocks Calendars
- Linear & Quadratic Equations
- Functions
- English Grammar
- General Awareness