The average of the numbers 10, 12, 15, 16, and 20 can be calculated by summing the values and dividing by ___ .

5

True or False: The average of a set of numbers is always equal to the median of the same set.

False; the average is not always equal to the median, especially in skewed distributions.

If the sum of the numbers 20, 30, and 50 is 100, what is the average of these numbers?

The average is 100 / 3 = 33.33.

If the average of 5 quantities is 20, what is the sum of these quantities?

The sum of these quantities is 20 x 5 = 100.

True or False: If a new member replaces an existing member and the average age increases, the new member's age is calculated by adding the product of the increase in average and the total number of people to the age of the person who left.

True.

When a person travels a distance at speeds of x km/hour and y km/hour, the average speed during the journey is calculated using the formula: ___

The average speed = (2xy) / (x + y).

If the average score of a batsman after 16 innings is 36 and he scores 70 in the next inning, what will be his new average?

The new average will be 38, calculated by taking the sum of runs after 17 innings (576 + 70 = 646) and dividing by the total number of innings (646 / 17 = 38).

The average age of 29 students is 18 years. If the teacher's age is included and the new average becomes 18.2, what is the age of the teacher?

The age of the teacher is 28 years, calculated by finding the total age of students (29 × 18 = 522) and the new total age including the teacher (30 × 18.2 = 546), then subtracting the total age of students from the new total (546 - 522 = 24).

If the average age of 29 students is 18 years, what is the total age of all 29 students?

The total age of all 29 students is 522 years, calculated as 18 × 29.

When a teacher is included, and the average age becomes 18.2 years for 30 individuals, what is the age of the teacher?

The age of the teacher is 24 years, calculated by finding the total age for 30 individuals (30 × 18.2 = 546) and subtracting the total age of students (546 - 522 = 24).

If the average of 8 persons is x years and it increases by 2 years when a 24-year-old is replaced, then the age of the new person is ___ years.

40 years

Calculate the average runs made by Viraj in his last 7 matches given that his total runs in 15 matches is 642 and in the first 8 matches is 443.2.

28.4