# ISS (Statistical Services) Statistics Paper IV: Questions 42 - 45 of 79

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## Question number: 42

» Demography and Vital Statistics » Standardized Death Rates

### Describe in Detail

Compute the crude and standardized death rates of the populations A and B, regarding A as standard population, from the following data:

Age groups (years) | A | B | ||

Population | Deaths | Population | Deaths | |

Under 10 | 20000 | 600 | 12000 | 372 |

10 - 20 | 12000 | 240 | 30000 | 660 |

20 - 40 | 50000 | 1250 | 62000 | 1612 |

40 - 60 | 30000 | 1050 | 15000 | 525 |

Above 60 | 10000 | 500 | 3000 | 180 |

### Explanation

From the given data, the crude death rate for any population is

For population A

For population B

The standardized death

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## Question number: 43

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Following data gives the diameter of the rings manufactured by a company. Obtain the Control limits for R-chart.

Sample No. | Observations | ||||

1 | 5.02 | 5.01 | 4.94 | 4.99 | 4.96 |

2 | 5.01 | 5.03 | 5.07 | 4.95 | 4.96 |

3 | 4.99 | 5.00 | 4.93 | 4.92 | 4.99 |

4 | 5.03 | 4.91 | 5.01 | 4.98 | 4.89 |

5 | 4.95 | 4.92 | 5.03 | 5.05 | 5.01 |

6 | 4.97 | 5.06 | 5.06 | 4.96 | 5.03 |

7 | 5.05 | 5.01 | 5.10 | 4.96 | 4.99 |

8 | 5.09 | 5.10 | 5.00 | 4.99 | 5.08 |

9 | 5.14 | 5.10 | 4.99 | 5.08 | 5.09 |

10 | 5.01 | 4.98 | 5.08 | 5.07 | 4.99 |

### Explanation

Sample No. | Observations | Total | Sample Mean | Range | ||||

1 | 5.02 | 5.01 | 4.94 | 4.99 | 4.96 | 24.92 | 4.98 | 0.08 |

2 | 5.01 | 5.03 | 5.07 | 4.95 | 4.96 | 25.02 | 5.00 | 0.12 |

3 | 4.99 | 5.00 | 4.93 | 4.92 | 4.99 | 24.83 | 4.97 | 0.08 |

4 | 5.03 | 4.91 | 5.01 | 4.98 | 4.89 | 24.82 | 4.96 | 0.14 |

5 | 4.95 | 4.92 | 5.03 | 5.05 | 5.01 | 24.96 | 4.99 | 0.13 |

6 | 4.97 | 5.06 | 5.06 | 4.96 | 5.03 | 25.08 | 5.02 | 0.10 |

7 | 5.05 | 5.01 | 5.10 | 4.96 | 4.99 | 25.11 | 5.02 | 0.14 |

8 | 5.09 | 5.10 | 5.00 | 4.99 | 5.08 | 25.26 | 5.05 | 0.11 |

9 | 5.14 | 5.10 | 4.99 | 5.08 | 5.09 | 25.40 | 5.08 | 0.15 |

10 | 5.01 | 4.98 | 5.08 | 5.07 | 4.99 | 25.13 | 5.03 | 0.10 |

Total | 50.11 | 1.15 |

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## Question number: 44

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2013

### Describe in Detail

For a PBIB design with parameters**, **b, r, k**, ****, **show that

### Explanation

A PBIB design with m associate classes based on the association scheme is an arrangement of treatments into b blocks such that

(i) Each block contains k distinct treatments (k <

(ii) Each treatment occurs in r blocks

(iii) Any two treatments, which are ith associates occur together in blocks (i = 1,2, . . , m) are called the parameters

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## Question number: 45

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2012

### Describe in Detail

Discus symmetrical BIBD. For an SBIBD, under usual notations, show that

=

### Explanation

**Symmetrical BIBD**:

A BIBD is said to be symmetric if b= υ and r = k.

υ, r, b, k and λ are called the parameters of the BIBD

υ= number of varities or treatments

b = number of blocks

r = number of replicates for each treatment

k = block size

λ=number of blocks in which any pair of treatments occurs together

**Proof: ****=**

Let N be the in

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