B1.
The Standard Deviation is 3.78497.
The Variance is 14.326.
The Range is 31.07.
B2.
- The values of the median and mode are 18.78 and 18.65.
- Yes, they are the same.
- The quartile values are 17.16(Q1) and 21.21(Q3)
- The value of the IQR is: 21.21-17.16 = 4.05
- In this case, the Mode is 18.65, the Median is 18.78 and the Mean is 19.68. The mean age at first birth is nearly a full year more than the media, means that the distribution is positively skewed.
B3.
- The value of the trimmed mean is 19.3477. The value arrived at by dropping 5% from the lower end of the distribution and 5% from the upper end. Yes, the trimmed mean and the untrimmed mean are different.
- This table indicated IQR and it is 4.05. It is the same as my own calculations in exercise B2.
- The index of the skewness is 1.558 and a standard error is 0.08. The skewness index is more than twice the value of its standard error, which can be interpreted as a departure from symmetry (suggest a skew). It has a positive skewed distribution (right side).
- The kurtosis index is 3.75, indicates the distribution is leptokurtic.
- Case 890 (ID18329) has the highest value of 42.32. Case 729(ID16560) has the lowest value of 11.25.
- Yes, there are many outliners. They are all at the upper end of the distribution. I am not sure about the number of outliers, if all the points with ID numbers in this boxplot are above the upper edge. The number could be 17.
The IQR is 4.05 and the Q3 is 21.21.
21.21+ (1.5 x 4.05)= 27.285
21.21+(3 x 4.05) = 33.36
So if the data value lies between 27.285-33.36, it is a mild outlier. If the data value lies above 33.36, it is an extreme outlier. Because the boxplot is not clear enough, so I couldn’t count how many cases are mild and how many cases are extreme.
- The case ID 18329 is the most extreme one, and her age at first birth is 42.32. The first birth in this age is possible so they are not likely to be data entry errors.
B4.
- The mean is 1.5019 and the SD is 0.86431. The range is 7.83. This information means
- The name is “zcrowded”.
- The mean is 0 and the SD is always 1.
- For the first person, the value of crowded is 1.33(average is 1.5). This indicates her situation was more crowded. And the standard score for crowded is -0.19501. It is just slightly lower than 1 SD below the mean, only 1/5 a standard deviation.
B5.
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Table 1 Background Characteristics of Study Participants | ||||
N |
Mean | SD | Range of Values | |
Age at first birth (years) | 929 | 19.7 | 3.8 | 11.3-42.3 |
Age (years) | 1000 | 36.6 | 6.2 | 19.4-49.4 |
Highest school grade completed | 989 | 11.3 | 1.6 | 1-16 |
Total people living in household past month | 1000 | 4.1 | 1.8 | 1-12 |
Family income($) | 895 | 1,172.6 | 788.2 | 0-6,593 |