Question

The Cambridge Study in Delinquent Development was undertaken in north London (U.K.) to investigate the links between criminal behavior in young men and the socioeconomic factors of their upbringing (Farrington 1994). A cohort of 395 boys was followed for about 20 years, starting at the age of 8 or 9. All of the boys attended six schools located near the research office. The following table shows the total number of criminal convictions by the boys between the start and end of the study. Number of Convictions Frequency 0 265 1 49 2 21 3 19 4 10 5 10 6 2 7 2 8 4 9 2 10 1 11 4 12 3 13 1 14 2 Total: 395

Answer 1

1. The table is a frequency distribution table.

2. The variable presented in the table is Number of convictions

3. The number of boys who have exactly 2 conviction = Frequency corresponding to the number of convictions 2

= 21

4. Number of boys who had no convictions = 265

Total number of boys = 395

Percentage of boys who had no convictions = $\frac{265}{395}*100=67.08\approx 67$

ANS: The percentage of boys who had no conviction = 67%

5. The Frequency distribution is skewed. ( positively)

(as seen from the graph)

6. The frequency distribution is Unimodal. ( Here the mode { highest frequency } occurs only at 0 )

7.  Q1 is the 1/4*(N+1)th value = 395+1/4=396/4=99th value. where N = Total frequency =395

thus, Q1 = 0

Q3 is the 3/4*(N+1)th value = 3*(395+1)/4=3*396/4=297th value.

thus, Q3 = 1

Inter Quartile range =IQR= Q3-Q1=1-0=1

we can say that the values lying outside the range of (Q1-1.5*IQR,Q3+1.5*IQR) are potential outliers.

since (0-1.5*1,1+1.5*1)=(-1.5,2.5) So, the rest are detected potential outliers.

Hence YES there are outliers.

8. No, the sample doesnot represent a random sample.