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:

  1. 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]

  2. 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]

  3. 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.

Thanks for taking the time to read What is the standard deviation of the following numbers 1 33 1 34 1 42 1 51 1 53 1 61 1 69 1 71. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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