The weight of 10 students are given below, find the modal weight.
| Weight (kg) | 33 | 35 | 37 | 39 | 42 |
|---|---|---|---|---|---|
| No. of students | [tex]$x$[/tex] | [tex]$x+1$[/tex] | [tex]$2x$[/tex] | [tex]$3x-2$[/tex] | [tex]$x+3$[/tex] |
Answer (2)
The modal weight of the students is 42 kg, as it is the weight that has the highest number of students (4). This was determined by solving for the variable x , which allowed us to distribute the total number of students across the different weights and identify the most frequent one.
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Set up an equation to find the value of x : x + ( x + 1 ) + 2 x + ( 3 x − 2 ) + ( x + 3 ) = 10 .
Solve for x : x = 1 .
Substitute x to find the number of students for each weight: 33 kg (1 student), 35 kg (2 students), 37 kg (2 students), 39 kg (1 student), 42 kg (4 students).
Identify the modal weight: 42 kg .
Explanation
Understanding the Problem We are given the weights of 10 students and the number of students for each weight in terms of x . Our goal is to find the modal weight, which is the weight with the highest frequency (i.e., the weight that appears most often).
Setting up the Equation First, we need to find the value of x . We know that the total number of students is 10. So, we can set up an equation by summing the number of students for each weight and equating it to 10: x + ( x + 1 ) + 2 x + ( 3 x − 2 ) + ( x + 3 ) = 10
Solving for x Now, let's solve the equation for x : x + x + 1 + 2 x + 3 x − 2 + x + 3 = 10 Combining like terms, we get: 8 x + 2 = 10 Subtracting 2 from both sides: 8 x = 8 Dividing by 8: x = 1
Finding the Number of Students for Each Weight Now that we have the value of x , we can find the number of students for each weight by substituting x = 1 into the expressions given in the table:
Weight 33 kg: x = 1 student
Weight 35 kg: x + 1 = 1 + 1 = 2 students
Weight 37 kg: 2 x = 2 ( 1 ) = 2 students
Weight 39 kg: 3 x − 2 = 3 ( 1 ) − 2 = 1 student
Weight 42 kg: x + 3 = 1 + 3 = 4 students
Identifying the Modal Weight Finally, we identify the weight with the highest number of students. From the calculations above, we see that the weight 42 kg has the highest number of students, which is 4.
Conclusion Therefore, the modal weight is 42 kg.
Examples
Understanding modal weight is useful in various real-life scenarios. For example, in a shoe store, the modal shoe size helps the store owner to stock more of the most frequently sold size, optimizing inventory and customer satisfaction. Similarly, in manufacturing, knowing the modal dimension of a part helps in quality control by focusing on the most common measurement, ensuring consistency and reducing defects. In education, identifying the modal test score can help teachers understand the most common level of understanding among students and adjust their teaching methods accordingly.
