Answers

1. a) 10; b) 2.8; c) 11.3; 3.4; d) 6; 2. a) 29.52; 5.43; b) 4.75; c) 15;

d) 10; 3. a) 10325.9; b) 305; c) 82.25; d) 156.5;

4. a) 10; b) 9; c) 3; 5. ; b) ; c) ;

6. ; ; ; 7. for both data sets;

8. and ; 9. 45; 43.5; 50; ; ; 10. a) 550-1050; b) 700-900; 11. a) 23.000-35.000;

b) 23.000-35.000; 12. a) ; b) ;

13. $4.84-$5.20; 14. 89-101; 15. a) 37.000-53.000.

Numerical summary of grouped data

Mean for data with multiple-observation values

Suppose that a data set contains values occurring with frequencies, respectively.

1. For a population of observations, so that

The mean is

2. For a sample of observations, so that

The mean is

The arithmetic is most conveniently set out in tabular form.

Example:

The score for the sample of 25 students on a 5-point quiz are shown below. Find the mean.

Score	Frequency

Solution:

We must find . We need a column to display the computation of the quantity (Table 1.3):

Table 1.3

Score	Frequency
		0· 1=0 1· 2=2 2· 6=12 3· 12=36 4· 3=12 5· 1=5

In the end, .

Hence the mean of the scores

Is approximately 2.7.

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