In: Statistics and Probability
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 |
# 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)?
# 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.