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The prime numbers between 30 and 50 are 31, 37, 41, 43, and 47. To find the average, sum these values (31+37+41+43+47 = 199) and divide by the count of numbers (5), resulting in 199/5 = 39.8.
The sum of the ages of the first 3 friends is 3 * 23 = 69. With the 4th friend, the total number of people is 4, and the average is 23, so the new sum is 4 * 23 = 92. The age of the 4th friend is 92 - 69 = 23 years.
The arithmetic mean, commonly known as the average, is defined as the sum of all observations in a data set divided by the total number of observations. Because every individual data point contributes to the sum, the arithmetic mean is dependent on all values within the set to provide an accurate representation of the central tendency.
Let the average expenditure be 'x'. The total expenditure is 9x. The sum of expenditures is (8 * 12) + (x + 8) = 9x. Solving 96 + x + 8 = 9x leads to 104 = 8x, so x = 13. The total expenditure is 9 * 13 = 117.
First, calculate the total age of the 32 students: 32 multiplied by 10 equals 320. When the teacher is added, the group size becomes 33 and the average age becomes 11. The new total age is 33 multiplied by 11, which is 363. Subtracting the initial total from the new total (363 - 320) gives the teacher's age as 43 years.
The average of a set of numbers is the sum of the numbers divided by the count. Here, (5 + 6 + 7 + w) / 4 = 10. Multiplying by 4 gives 5 + 6 + 7 + w = 40. Simplifying the sum, 18 + w = 40, which leads to w = 22.
The arithmetic mean of a set of numbers is calculated by finding the sum of the numbers and dividing by the count of the numbers. For the set {4, 6}, the sum is 4 + 6 = 10. Dividing by the count, which is 2, gives 10 / 2 = 5.
The initial sum of the 6 numbers is 6 * 8.5 = 51. After removing one number, the sum of the remaining 5 numbers is 5 * 7.2 = 36. The difference between the initial sum and the new sum is 51 - 36 = 15.
The median is the middle value of a sorted data set. Since there are 9 values (an odd number), the median is the value at the (n+1)/2 position. Here, (9+1)/2 = 5th position. Counting through the ordered list, the 5th value is 14.
The mean of a set of observations is defined as the sum of the observations divided by the total number of observations. Therefore, the sum can be calculated by multiplying the mean by the number of observations: 20 × 15 = 300.
