Question

Find the variance for the given data. Round your answer to one more decimal place than the original data.

13.9 12.0 13.0 12.3 10.5
A. 1.27
B. 1.59
C. 1.49
D. 33.32

Answer 1

To find the variance of the data set (13.9, 12.0, 13.0, 12.3, 10.5), calculate the mean, subtract it from each data point to get deviations, square these deviations, and then average them. By rounding to the correct significant figures, the variance is 1.60. Option number b is correct.

Step-by-step explanation:

To find the variance for the given data set (13.9, 12.0, 13.0, 12.3, 10.5), we need to follow these steps:

1. Calculate the mean (average) of the data.
2. Subtract the mean from each data point to find the deviations.
3. Square each deviation to make them positive.
4. Find the average of these squared deviations to get the variance.

Let's carry out these steps:

1. Mean: (13.9 + 12.0 + 13.0 + 12.3 + 10.5) / 5 = 61.7 / 5 = 12.34
2. Deviations: (13.9-12.34), (12.0-12.34), (13.0-12.34), (12.3-12.34), (10.5-12.34)
3. Squared Deviations: 2.4481, 0.1156, 0.4356, 0.0016, 3.3936
4. Variance: (2.4481 + 0.1156 + 0.4356 + 0.0016 + 3.3936) / 4 = 6.3945 / 4 = 1.598625

According to the rules of significant figures and rounding, since the original data is given to one decimal place, we need to round the variance to two decimal places. Therefore, the variance of the data set is 1.60.

Note: For calculating the variance, we divide by n-1 (where n is the number of data points) since it is a sample variance.