Answer :
To find the standard deviation of the given numbers 1.33, 1.34, 1.42, 1.51, 1.53, 1.61, 1.69, 1.71, 1.73, 1.81, we can follow these steps:
Calculate the Mean (Average):
The mean is calculated by summing all the numbers and dividing by the count of the numbers.
[tex]\text{Mean} = \frac{(1.33 + 1.34 + 1.42 + 1.51 + 1.53 + 1.61 + 1.69 + 1.71 + 1.73 + 1.81)}{10} = \frac{15.68}{10} = 1.568[/tex]
Calculate the Variance:
Variance is the average of the squared differences from the mean.
First, calculate each difference from the mean, square it, and find the average of these squared differences:
[tex]\text{Variance} = \frac{(1.33 - 1.568)^2 + (1.34 - 1.568)^2 + (1.42 - 1.568)^2 + \ldots + (1.81 - 1.568)^2}{10}[/tex]
Calculating each difference, squaring them, and summing them:
[tex]= \frac{(0.238^2) + (0.228^2) + (0.148^2) + (0.058^2) + (0.038^2) + (0.042^2) + (0.122^2) + (0.142^2) + (0.162^2) + (0.242^2)}{10}[/tex]
[tex]= \frac{0.056644 + 0.051984 + 0.021904 + 0.003364 + 0.001444 + 0.001764 + 0.014884 + 0.020164 + 0.026244 + 0.058564}{10} = 0.0186[/tex]
Calculate the Standard Deviation:
The standard deviation is the square root of the variance:
[tex]\text{Standard Deviation} = \sqrt{0.0186} \approx 0.136[/tex]
The standard deviation of the numbers is approximately 0.136. This value indicates how much the numbers deviate, on average, from the mean.
