# ISS (Statistical Services) Statistics Paper IV: Questions 24 - 27 of 92

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## Question number: 24

» Demography and Vital Statistics » Abridged Life Tables

### Describe in Detail

Describe king’s method for constructing an abridged life table.

### Explanation

An abridged life table consists of all columns of a life table for ages distant apart usually 5 to 10 years or for age groups usually of width 5 to 10 years. In this way there is tremendous cut in size of life-tables, and hence such life tables are named as abridged life table.

Central mortality rate can be calculated precisely provided the populati

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## Question number: 25

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

a) If the average range for the 4 samples is 0.2 millimeters and the average mean of the observations is 12.5 millimeters, obtain the three-sigma control limits for the sample mean.

b) 5 observations have been taken from the10 samples in order to test the volume in the bags. The average sample range is 0.5 ounces. Obtain the 3-σ limits for the sample range.

### Explanation

a) It is given that n = 5 and

Based on tables for control charts. For n = 5, The value of

Control limits for :

And

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## Question number: 26

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

A new oven has been installed in a bakery and to test the efficiency of this, the oven temperature readings have been taken at four different places inside the oven every 30 min. The following table gives readings. Determine the control limits for the mean temperature.

Time | Readings | |||

8: 00 | 400 | 500 | 550 | 390 |

8: 30 | 440 | 420 | 380 | 380 |

9: 00 | 410 | 450 | 470 | 430 |

9: 30 | 390 | 390 | 410 | 410 |

10: 00 | 370 | 420 | 460 | 410 |

10: 30 | 390 | 400 | 390 | 400 |

### Explanation

From the tables, for n = 6, we have

**Control limits for** **:**

And

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## Question number: 27

» Demography and Vital Statistics » Measurement of Fertility » Total Fertility Rate

### Describe in Detail

Compute GFR, SFR, TFR and GRR from the data given below:

Age groups of child bearing females | Number of women (‘000) | Total births |

15 - 19 | 16.0 | 260 |

20 - 24 | 16.4 | 2244 |

25 - 29 | 15.8 | 1894 |

30 - 34 | 15.2 | 1320 |

35 - 39 | 14.8 | 916 |

40 - 44 | 15.0 | 280 |

45 - 49 | 14.5 | 145 |

Assume that the proportion of female births is 46.2 percent.

### Explanation

First write the formula of GFR, SFR, TFR and GRR is

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