Question

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s,91 s,95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be:
A. $92\pm 2$ s
B. $92\pm 5$ s
C. $92\pm 1.8$ s
D. $92\pm 3$ s

Answer 1

We are given a set of data which is the observation for the time period of 100 oscillations of a simple pendulum. But they had also provided the minimum division in the measuring clock. If this would not have been provided, we would have simply added all the observations and divided by the number of observations.

Complete step by step answer:
The given observations are: 90, 91, 95, 92
Sum of all observations= 90+ 91+ 95+ 92= 368
Number of observations= 4
Average = 368/4= 92
Now, sum of modulus errors in the data= 2+1+3= 6
Average error= 6/4 = 1.5
Rounding to the next decimal place we get 2.

Hence the correct option is A.

Additional information:
Mean is also said to be arithmetic mean. The meaning of mean is to evaluate the average. It is defined as the average of the given numbers. Mean is the sum of all the given data values divided by the total number of data values given in the set. It is given by:
Mean = Sum of Observations/Total number of observations
A mean is simply defined as the average of the given set of numbers. The mean is also considered as one of the measures of central tendencies in Statistics. It gives the central value of the set of values. The other two measures of central tendency are median and mode. Many students get confused with these three terms.

Note: Absolute Error is defined as the amount of error in the measurement. It is the difference between the measured value and true value. The absolute error of the sum or difference of a number of quantities is less than or equal to the sum of their absolute errors. On the other hand, the Mean Absolute Error (MAE) is the average of all absolute errors. The mean absolute error uses the same scale as the data being measured.