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Marizza181 [45]

3 years ago

10

A pharmacist weighed eight different capsules of the same compound and recorded these measurements: 2312 mg, 2313 mg, 2315 mg, 2

321 mg, 2325 mg, 2310 mg, 2320 mg, and 2319 mg. What is the median measurement? What is the mean measurement?

1 answer:

Orlov [11]3 years ago

8 0

median = 2317

mean = 2,316.875

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kati45 [8]

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Given:

$\sigma_A=3$

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$\sigma_B=5$

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Solution:

Formula for variance is

$\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}$ ...(i)

Using (i), we get

$\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}$

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Similarly,

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$100=\sum (x_i-\overline{x}_B)^2$

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$\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}$

$\sigma^2=\dfrac{54+100}{6+4}$

$\sigma^2=\dfrac{154}{10}$

$\sigma^2=15.4$

Therefore, the variance of combined set is 15.4.

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