Question

In: Statistics and Probability

Problem set 2: use the following table to answer questions 4-7 (40 pts total): # of...

Problem set 2: use the following table to answer questions 4-7 (40 pts total):

# of children

Frequencies

0

472

1

218

2

175

3

320

4

187

5

128

6

47

7

33

8

20

N

1,600

  1. Please find the mean for numbers of children in this distribution (20 pts).

# of children

Frequencies

How many # of children in each category:

# of Children * Freq. in each column

0

472

0*472=0

1

218

2

175

3

320

4

187

5

128

6

47

7

33

8

20

Total Categories= 9

Total respondents in this data set is 1,600 (N)

Sum all above=               /1600=

5.Please find the median for this distribution (10 pts).

6.Please find the mode for this distribution (5 pts).

7. Is this distribution negatively skewed, symmetrical, or positively skewed (5 pts)?

Solutions

Expert Solution

# of children x

Frequencies f

f*x

cumulative frequency

0

472

0

472

1

218

218

690

2

175

350

865

3

320

960

1185

4

187

748

1372

5

128

640

1500

6

47

282

1547

7

33

231

1580

8

20

160

1600

Total

1,600

3589

4. Please find the mean for numbers of children in this distribution (20 pts).

=2.2431

5.Please find the median for this distribution (10 pts).

Total n=1600,therefore 1600/2 = 800

Median is average of 800 and 801th observation.

From cumulative frequency, 800 and 801th observations are 2.

Median =2

6.Please find the mode for this distribution (5 pts).

Mode most frequently occurred= 0

Mode=0

7. Is this distribution negatively skewed, symmetrical, or positively skewed (5 pts)?

Mean =2.24, median =2 mode =0

Mean > median >mode.

Since, Mean > median >mode, this distribution is positively skewed.


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