Question

A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on the area of scleral lamina (mm) from human optic nerve heads: 2.79 2.56 2.70 3.83 2.36 2.69 3.99 4.31 3.96 4.40 3.45 4.46 2.44 3.57 2.82 3.47 2.99 (a) Calculate Σχί and Σχί2. (Round Σχί2 to two decimal places.) mm2 mm4 (b) Use the values calculated in part (a) to compute the sample variance s2 and then the sample standard deviation s. (Round your answers to three decimal places.) mm4 mm2 SF Need Help?ReadIt Talk to a Tutor

Answer 1

${\color{Blue} \mathbf{Solution}}$

${\color{Blue} \boldsymbol{(a)}}\;$

$\sum X_i=\mathbf{{\color{Red} 56.79}}\;mm^{2}$

$\sum X_i^{2}=\mathbf{198.0661}\approx \mathbf{{\color{Red} 198.07}}\;mm^{4}$

${\color{Blue} \boldsymbol{(b)}}\;$

$sample \;variance\;(s^{2})=\frac{\sum X_i^{2}-\frac{\left ( \sum X_i \right )^{2}}{n}}{n-1}$

$sample \;variance\;(s^{2})=\frac{198.07-\frac{\left (56.79\right )^{2}}{17}}{17-1}$

$sample \;variance\;(s^{2})=\mathbf{{\color{Red} 0.522}}\;mm^{4}$

$\\sample \;standard \;deviation\;(s)=\sqrt{sample\;variance}=\sqrt{0.522}=\mathbf{{\color{Red} 0.723}}\;mm^{2}$