Question

The mean weight of 9 students is \(25 \mathrm{~kg}\). If one more student is joined in the group the mean is unaltered, then the weight of the 10th student is (1) 25 (2) 24 (3) 26 (4) 23

Short answer

Answer: The weight of the 10th student is 25 kg.

Step-by-step solution

Find the total weight of the 9 students

We are given that the mean weight of 9 students is \(25 \mathrm{~kg}\). The formula for mean is: Mean = (Total weight of students) / (Number of students) Let's denote the total weight of the 9 students as W. We can write the equation for the mean as follows: \(25 = W / 9\) Now, we need to find the total weight W by solving for W in the equation above. \(W = 25 * 9\) \(W = 225 \mathrm{~kg}\) The total weight of the 9 students is \(225 \mathrm{~kg}\).

Find the weight of the 10th student

We are given that the mean weight remains the same when the 10th student joins the group. Let's denote the weight of the 10th student as x. The total weight of 10 students will be W + x. The mean formula for the 10 students will be: Mean = (Total weight of 10 students) / (Number of students) \(25 = (225 + x) / 10\) Now, we need to find the weight of the 10th student (x) by solving for x in the equation above. \(25 * 10 = 225 + x\) \(250 = 225 + x\) Subtract \(225\) from both sides to solve for x: \(x = 250 - 225\) \(x = 25 \mathrm{~kg}\) The weight of the 10th student is 25 kg, which corresponds to the first answer choice (1) 25.

Key concepts

Weight Calculation

Understanding weight calculation is crucial when solving problems related to averages or means. In this context, the mean weight of students helps us determine the total weight and subsequently individual weights.
The mean is commonly used in daily life to describe data sets. The formula to calculate the mean is straightforward:

• Mean = (Total sum of all weights) / (Number of individuals)

For our problem, we first identify the mean weight of 9 students as 25 kg. To find the total weight of these students, we rearrange the formula to solve for total weight:

• Total Weight = Mean x Number of Students

Thus, when given the mean and the number of individuals, we can easily calculate the total weight, which provides the basis for further calculations involving any additional participants. Always remember that weight calculations form the foundation of understanding averages, especially when adjustments to group size are involved.

Algebraic Equations

Algebraic equations are a powerful tool in simplifying and solving many types of problems, including those involving averages and means.
In our exercise, we deal with an equation that helps us find the weight of the 10th student joining a group of 9 students. The goal is to set up the equations based on the given data and solve for the unknown variable.
Here's how we set it up:

• First, the original mean formula:
  • Mean = (Total Weight of 9 Students) / 9

We know the total weight (W) is 225 kg since Mean = 25 kg. For the 10th student, the equation becomes:

• Mean = (Total Weight of 10 Students) / 10

This translates to solving the equation:\[25 = \frac{225 + x}{10}\]By solving, we determine that the weight of the 10th student (x) keeps the mean constant. Understanding this algebraic step allows us to efficiently find unknowns in various scenarios that involve incremental changes to data sets.

Problem Solving

Problem solving often requires a blend of understanding concepts, applying logical steps, and using mathematical tools. With this exercise, we're tasked with determining the weight of a new student in a group while maintaining the given mean.
To solve this kind of problem effectively:

• Analyze what the problem is asking: Here, determine the weight of the new student.
• Identify the known elements: Mean of 9 students and that it remains unchanged with the 10th addition.
• Apply the relevant formulae: Use mean calculation and algebraic manipulation to solve for the unknown variable.

These structured steps make sure you aren't overwhelmed by the problem, as they guide you through logical reasoning. This helps you arrive at the correct solution, maintaining the integrity of the problem's conditions, such as keeping the mean constant. Effective problem solving is a skill honed with practice, but with each solution, these tasks become increasingly manageable and less daunting.