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2 years ago

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Quality control is an important issue at ACME Company which manufacturers light bulbs. In order to conduct testing of the life h

ours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, and 321. What is the Variance?

1 answer:

mrs_skeptik [129]2 years ago

4 0

Answer: 3424.28

Step-by-step explanation:

Given data : 378, 361, 350, 375, 200, 391, 375, 368, 321

Number of data values = 9

Mean : $\overline{x}=\dfrac{\sum^n_{i=1} x_i}{n}$

$\\\\=\dfrac{378+361+350+375+200+391+375+368+321}{9}\\\\=\dfrac{3119}{9}\approx346.56$

Variance = $\dfrac{\sum^n_{i=1} (x_i-\overline{x})^2}{n-1}$

$\sum^n_{i=1} (x_i-\overline{x})^2 = (31.44)^2+(14.44)^2+(3.44)^2+(28.44)^2+(-146.56)^2+(44.44)^2+(28.44)^2+(21.44)^2+(-25.56)^2\\\\=27394.2224$

Variance = $\dfrac{27394.2224}{8}=3424.2775\approx3424.28$

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