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Directions:

Read the following information and answer the three questions that follow:

The following data presents a count of released convicts who have served prison terms (X), those who have received some educational or technical training during their term (Y), and those who were offered company placement (Z) respectively, from six different jails A, B, C, D, E, and F, in the year 2010

X

Y

Z

A

86

45

25

B

1305

903

461

C

2019

940

474

D

1166

869

416

E

954

544

254

F

1198

464

174

Jails with highest and smallest percentage of trained convicts are respectively:

This question was previously asked in
CDS I 2020 Elementary Mathematics Previous Year Paper (02-Feb-2020)
The correct answer is

D and F

Analyzing Convict Data and Training Percentages

The question asks us to identify the jails with the highest and the smallest percentage of trained convicts out of the total released convicts. We are provided with data for six jails (A, B, C, D, E, F) showing the number of released convicts (X) and those who received training (Y).

To find the percentage of trained convicts for each jail, we use the following formula:

Percentage of trained convicts \(= \left( \frac{\text{Number of trained convicts (Y)}}{\text{Total number of released convicts (X)}} \right) \times 100\)

Let's calculate the percentage for each jail using the data from the provided table:

Jail Released (X) Trained (Y) Calculation Percentage
A 86 45

\(\left( \frac{45}{86} \right) \times 100\)

\(\approx 52.33\%\)

B 1305 903

\(\left( \frac{903}{1305} \right) \times 100\)

\(\approx 69.19\%\)

C 2019 940

\(\left( \frac{940}{2019} \right) \times 100\)

\(\approx 46.56\%\)

D 1166 869

\(\left( \frac{869}{1166} \right) \times 100\)

\(\approx 74.53\%\)

E 954 544

\(\left( \frac{544}{954} \right) \times 100\)

\(\approx 57.02\%\)

F 1198 464

\(\left( \frac{464}{1198} \right) \times 100\)

\(\approx 38.73\%\)


Comparing Training Percentages Across Jails

Now, let's compare the calculated percentages for each jail:

  • Jail A: \(\approx 52.33\%\)
  • Jail B: \(\approx 69.19\%\)
  • Jail C: \(\approx 46.56\%\)
  • Jail D: \(\approx 74.53\%\)
  • Jail E: \(\approx 57.02\%\)
  • Jail F: \(\approx 38.73\%\)

By examining these percentages, we can find the highest and smallest values:

  • The highest percentage of trained convicts is approximately \(74.53\%\), which corresponds to Jail D.
  • The smallest percentage of trained convicts is approximately \(38.73\%\), which corresponds to Jail F.

Therefore, the jails with the highest and smallest percentage of trained convicts are D and F, respectively.

Revision Table: Key Calculations

Here is a summary of the calculated percentages for quick reference:

Jail Percentage of Trained Convicts (approx.)
A 52.33%
B 69.19%
C 46.56%
D 74.53%
E 57.02%
F 38.73%

Highest percentage: Jail D (74.53%)

Smallest percentage: Jail F (38.73%)

Additional Information: Understanding Convict Rehabilitation Data

This type of data analysis helps in evaluating the effectiveness of training programs in different correctional facilities. The percentage of trained convicts shows the proportion of released individuals who received educational or technical training during their term. A higher percentage might indicate a greater emphasis on rehabilitation through skill development in that particular jail. Comparing these percentages across different jails allows for insights into varying approaches to inmate training. It's important to note that this data only reflects the number of individuals trained and released; it doesn't directly measure the success of these programs in terms of reducing recidivism or securing employment, although related data (like 'offered company placement - Z') might provide further context for a broader analysis.

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