How to Calculate Percent Error

Question 1: Mr. Raju measured his height and found 6 feet. But later on, by careful observation, he has found his actual height to be 5.5 ft. Find the percent error Raju made in measuring his height.

Solution:

Before solving the problem, let us identify the information,

Actual value = 5.5 ft and Estimated value = 6 ft.

Now,

Step 1: Subtract one value from others to get the absolute value]e of error.

Error = 6 – 5.5

= 0.5

Step 2: Divide the error by actual value.

0.5/5.5 = 0.0909 (up to 4 decimal places)

Step 3: Multiply that answer by 100 and attach the % symbol to express the answer as a percentage

0.0909 × 100 = 9.09%

Therefore Percentage error measured is 9.09% 

Question 2: Lakshmi’s mathematical class had 34 children yesterday. She miscounted the class total and recorded it as 28 children. What is Lakshmi’s percent error?

Solution:

The actual number of students = 34 

Recorded number of students = 28

Absolute Error = 34 – 28 = 6

Percent Error = 6/28 = 0.21

= 0.21 × 100 = 21%

Lakshmi’s percent error is 21% 

Question 3: A boy measured the area of a rectangle plot to be 450 cm². But the actual area of the plot has been recorded as 455 cm². Calculate the percent error of his measurement.

Solution:

Given,

Measured area value = 450 cm² 

Actual area value = 455 cm²

Steps of calculation,

Step 1: Subtract one value from another; 455 – 450 = 5

the difference is 5, which is the error.

Step 2: Divide the error by actual value; 5/455 = 0.0109

Step 3: Multiply this value by 100

0.0109 × 100 = 0.109% (expressing it in two decimal points)

Hence, 0.10% is the percent error. 

Question 4: A scale measures wrongly a value as 21 cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 17 cm.

Solution:

Given in the problem,

Recorded measurement = 21 cm

Actual measurement = 17 cm 

Error = Recorded measurement – Actual measurement 

= 21 – 17 = 4

Applying the formula for the computation,

Percentage Error = (Error) / (Actual measurement) × 100

= (4/17) × 100 = 0.235 × 100 = 23.5

Percentage Error calculated as 23.5% 

Question 5: John expected 30 people to turn up for a job interview, but only 24 did. What was the percentage error?

Solution:

The actual number of people attended = 24

Number of people expected = 30

Absolute Error = 30 – 24 = 6

Percent Error = 6/24= 0.25

= 0.25 × 100 = 25%

John’s percent error is 25%  

Question 6: Sam thought 90 people would turn up to the concert, but in fact, 100 did. What would be Sam’s percent error?

Solution: 

The actual number of people came to concert = 100

Number of people Sam expected = 90

Error = Expected number of people attended – Actual number of people 

= 100 – 90 = 10

Applying the formula for the computation,

Percentage Error = (Error) / (Actual measurement) × 100

= (10/90) × 100 = 0.235 × 100 = 23.5

Percentage Error calculated as 23.5% 

Question 7: Shreya is attempting the precision of a scale in her science lab. She took a weight that she knew had a mass of 30 kg and weighed it. The scale read that the weight weighed 30.4 kg. What is the absolute error of the mass of the weight that Shreya recorded? And also find percent error?

Solution:

Use the absolute error formula to determine this,

Absolute Error = |Actual Value – Measured Value|

Absolute Error = x

Actual Value = 30

Measured Value = 30.4

= |30 – 30.4| = |−0.4| = 0.4

The absolute error was 0.4 kg.

Percentage Error = (Error) / (Actual value) × 100

= (0.4/30) × 100

=1.3333% (Considering upto 2 decimal points)

Therefore Shreya’s percent error is 1.33%