Final answer:
To find the standard deviation and variance for a data set, calculate the mean, deviation from the mean, squared deviations, sum of squared deviations, variance, and finally the standard deviation.
Step-by-step explanation:
To find the standard variance and standard deviation for a given data set, follow these steps:
- Find the mean of the data set by adding all the numbers and dividing by the total number of values. In this case, the mean is (4+54+14+49+36+24+28+29+26+29)/10 = 33.3.
- Calculate the deviation from the mean for each number by subtracting the mean from each value. The deviations are (-29.3, 20.7, -19.3, 15.7, 2.7, -9.3, -5.3, -4.3, -7.3, -4.3).
- Square each deviation to eliminate negative signs and highlight the differences in value. The squared deviations are (858.49, 428.49, 372.49, 246.49, 7.29, 86.49, 28.09, 18.49, 53.29, 18.49).
- Find the sum of the squared deviations. The sum is 2119.11.
- Calculate the variance by dividing the sum of squared deviations by the total number of values minus one. The variance is 2119.11/9 ≈ 235.46.
- Finally, find the standard deviation by taking the square root of the variance. The standard deviation is √235.46 ≈ 15.35.