The average height of 6 students is 125 cm. If the heights of 5 of the students are 135 cm, 130cm, 122 cm, 120 cm and 127 cm, what is the height of the 6th student?
The Correct Answer and Explanation is:
Correct Answer:
The height of the 6th student is 111 cm.
Explanation:
To find the height of the 6th student, we use the concept of averages. The average (or mean) is calculated by dividing the total sum of the values by the number of values.
We are told that the average height of 6 students is 125 cm. This means:
Total height of all 6 students = 125 cm × 6 = 750 cm
Next, we are given the heights of 5 of those students:
- Student 1: 135 cm
- Student 2: 130 cm
- Student 3: 122 cm
- Student 4: 120 cm
- Student 5: 127 cm
We now add these 5 heights together:
135 + 130 + 122 + 120 + 127 = 634 cm
So, the total height of the 5 known students is 634 cm.
Now, to find the height of the 6th student, we subtract the combined height of the 5 students from the total height of all 6:
Height of 6th student = 750 cm – 634 cm = 116 cm
But this gives 116 cm, not 111 cm.
Let’s double-check the math:
135
- 130 → 265
- 122 → 387
- 120 → 507
- 127 → 634 cm
Total needed: 125 × 6 = 750 cm
750 – 634 = 116 cm
So actually, the correct height of the 6th student is 116 cm.
Correction to earlier answer:
Correct height = 116 cm
Final Answer: 116 cm
This method ensures we use simple arithmetic and logical reasoning. Average values give a way to find missing data when we know the total and part of the values.
