Question

You want to know the mean number of hours music students at your school practice each week. At each of three music classes you randomly survey 10 students. Your results are shown. Use all three samples to make one estimate for the mean number of hours music students practice each week. Round to the nearest hundredth if necessary. Hours Practiced Each Week A: 6, 5, 5, 6, 4, 6, 8, 5, 2, 6 B: 0, 6, 6, 5, 4, 5, 6, 3, 4, 9 C: 4, 5, 6, 4, 3, 2, 2, 3, 12, 1 The mean of all the sample data is hours.

Answer 1

The mean of a dataset is the average of the dataset

The mean of all the sample data is 4.67 hours

How to determine the mean

The datasets are given as:

Week A: 6, 5, 5, 6, 4, 6, 8, 5, 2, 6

Week B: 0, 6, 6, 5, 4, 5, 6, 3, 4, 9

Week C: 4, 5, 6, 4, 3, 2, 2, 3, 12, 1

The mean of a dataset is:

$\bar x = \frac{\sum x}{n}$

So, we have:

Week A

$\bar x_A = \frac{6+ 5+ 5+ 6+ 4+ 6+ 8+ 5+ 2+ 6 }{10}$

$\bar x_A =5.3$

Week B

$\bar x_B = \frac{0+ 6+ 6+ 5+ 4+ 5+ 6+ 3+ 4+ 9}{10}$

$\bar x_B = 4.8$

Week C:

$\bar x_C = \frac{4+ 5+ 6+ 4+ 3+ 2+ 2+ 3+ 12+ 1}{10}$

$\bar x_C = 4.2$

Calculate the mean for the three weeks

$\bar x = \frac{5.3 + 4.8 + 4.2}{3}$

$\bar x = 4.76$

Hence, the mean of all the sample data is 4.67 hours

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