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Contact [7]
3 years ago
9

The data to the right represent the weights​ (in grams) of a random sample of 50 candies. Complete parts​ (a) through​ (f). 0.92

0.92 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.
Mathematics
1 answer:
Inessa05 [86]3 years ago
5 0

Answer:

0.069

Step-by-step explanation:

The given data set is

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:

Mean=\frac{\sum x}{n}

Sum of all terms = 41.98

Mean of the data set is

Mean=\frac{41.98}{50}

Mean=0.8396

Formula for standard deviation for population:

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

Formula for standard deviation for sample:

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

\sigma=\sqrt{\frac{0.231792}{50-1}}

\sigma=\sqrt{0.004730449}

\sigma=0.06877826

\sigma\approx 0.069

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

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