what is the standard deviation for the data set? 212, 249, 212, 248, 239, 212, 216, 234, 248 express your…

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{212 + 249+212+248+239+212+216+234+248}{9}=\frac{2060}{9}\approx228.9$

Step2: Calculate the squared - differences

$(212 - 228.9)^2=(-16.9)^2 = 285.61$ $(249 - 228.9)^2=(20.1)^2 = 404.01$ $(212 - 228.9)^2=(-16.9)^2 = 285.61$ $(248 - 228.9)^2=(19.1)^2 = 364.81$ $(239 - 228.9)^2=(10.1)^2 = 102.01$ $(212 - 228.9)^2=(-16.9)^2 = 285.61$ $(216 - 228.9)^2=(-12.9)^2 = 166.41$ $(234 - 228.9)^2=(5.1)^2 = 26.01$ $(248 - 228.9)^2=(19.1)^2 = 364.81$

Step3: Calculate the variance

$s^{2}=\frac{285.61+404.01+285.61+364.81+102.01+285.61+166.41+26.01+364.81}{9 - 1}=\frac{2284.9}{8}=285.6125$

Step4: Calculate the standard deviation

$s=\sqrt{285.6125}\approx16.9$

Answer:

$16.9$