The average of a set of consecutive integers is calculated by taking the sum of the first and last terms and dividing by two. For the sequence 1 to 100, the calculation is (1 + 100) / 2 = 101 / 2 = 50.5. Note: The provided answer key indicates 50, which conflicts with the standard mathematical result of 50.5.
92
Calculate the arithmetic mean of the following set of numbers: 205, -101, 202, and -104.
To find the average, sum all the given values: 205 - 101 + 202 - 104 = 202. Then, divide this sum by the total count of numbers, which is 4. Dividing 202 by 4 results in 50.5.
93
Given the equation 16a + 16b = 48, what is the arithmetic mean of variables a and b?
Starting with the equation 16(a + b) = 48, we divide both sides by 16 to find that a + b = 3. The arithmetic mean of two numbers is defined as their sum divided by 2. Thus, the average is 3 divided by 2, which equals 1.5.
94
Given the following conditions: (i) P is taller than Q, (ii) R is shorter than P, (iii) S is taller than T but shorter than Q, determine who is the tallest among the group.
Based on the provided conditions, P is taller than Q and R. Since S is shorter than Q, and T is shorter than S, it follows that P is taller than all other individuals mentioned. Thus, P is the tallest person in the group.
95
Calculate the median of the following set of values: 5, 6, 7, 8, 9, 10, 11.
The median is the middle value of a data set when it is arranged in ascending order. The given set is already ordered: 5, 6, 7, 8, 9, 10, 11. Since there are 7 values, the median is the (7+1)/2 = 4th value. Counting to the fourth position, we find the value 8.
96
A group consisting of boys and girls has an average weight of 38 kg. If the average weight of 25 boys is 42 kg and the average weight of the girls is 33 kg, how many girls are in the group?
Let G be the number of girls. The total weight is (25 * 42) + (G * 33) = 38 * (25 + G). This expands to 1050 + 33G = 950 + 38G. Rearranging the terms gives 5G = 100, which results in G = 20. Thus, there are 20 girls in the group.
97
Determine the mode of the following data set: 2, 3, 3, 3, 4, 4, 5, 6.
The mode is defined as the value that appears most frequently in a data set. In the provided series, the number 3 appears three times, which is more frequent than any other number, making it the mode.
98
Calculate the arithmetic mean of the two expressions (x - 3) and (x + 5).
To find the arithmetic mean of two values, you sum them and divide by two. Adding (x - 3) and (x + 5) results in 2x + 2. Dividing this sum by 2 yields (2x + 2) / 2, which simplifies to x + 1.
99
If the mean of 10 numbers is 9.2, what is the total sum of these numbers?
The mean of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers. Therefore, the sum is equal to the mean multiplied by the count, which is 9.2 times 10, resulting in 92.
100
A class of 20 students has an average age of 14.95 years. When a new student joins the class, the average age increases to 15 years. What is the age of the new student?
To find the new student's age, calculate the total age before and after the arrival. The initial total age for 20 boys is 20 multiplied by 14.95, which equals 299. After the new student joins, there are 21 boys with an average age of 15, resulting in a total age of 315. The difference, 315 minus 299, equals 16 years.
