The data to the right represent the weights (in grams) of a random sample of 50 candies. Complete parts (a) through (f). 0.920.92 0.870.87 0.880.88 0.820.82 0.820.82 0.870.87 0.970.97 0.860.86 0.890.89 0.840.84 0.810.81 0.880.88 0.770.77 0.860.86 0.930.93 0.840.84 0.720.72 0.820.82 0.740.74 0.830.83 0.930.93 0.750.75 0.790.79 0.910.91 0.840.84 0.910.91 0.880.88 0.880.88 0.830.83 0.780.78 0.990.99 0.810.81 0.780.78 0.750.75 0.820.82 0.760.76 0.820.82 0.870.87 0.910.91 0.770.77 0.720.72 0.940.94 0.710.71 0.730.73 0.810.81 0.810.81 0.860.86 0.930.93 0.930.93 0.820.82 (a) Determine the sample standard deviation weight.

0.92, 0.87, 0.88, 0.82, 0.82, 0.87, 0.97, 0.86, 0.89, 0.84, 0.81, 0.88, 0.77, 0.86, 0.93, 0.84, 0.72, 0.82, 0.74, 0.83, 0.93, 0.75, 0.79, 0.91, 0.84, 0.91, 0.88, 0.88, 0.83, 0.78, 0.99, 0.81, 0.78, 0.75, 0.82, 0.76, 0.82, 0.87, 0.91, 0.77, 0.72, 0.94, 0.71, 0.73, 0.81, 0.81, 0.86, 0.93, 0.93, 0.82.

Formula for mean:

[tex]Mean=\frac{\sum x}{n}[/tex]

Sum of all terms = 41.98

Mean of the data set is

[tex]Mean=\frac{41.98}{50}[/tex]

[tex]Mean=0.8396[/tex]

Formula for standard deviation for population:

[tex]\sigma=\sqrt{\frac{\sum (x-\overline{x})^2}{n}}[/tex]

Formula for standard deviation for sample:

[tex]\sigma=\sqrt{\frac{\sum (x-\overline{x})^2}{n-1}}[/tex]

[tex]\sigma=\sqrt{\frac{0.231792}{50-1}}[/tex]

[tex]\sigma=\sqrt{0.004730449}[/tex]

[tex]\sigma=0.06877826[/tex]

[tex]\sigma\approx 0.069[/tex]

Therefore, the standard deviation of the data set is 0.069.