ACJC 2026 Sampling Summary

Anglo-Chinese Junior College 2026 H2 Mathematics 9758: Sampling / Summary / Page 1 of 1 SUMMARY: Sampling 1 Concept of Population and Sample 1. A population is the complete set of items being investigated. 2. A sample is a subset of a population. 3. A random sample of size n is a sample which is taken in such a way that every sample of size n of the population has an equal chance (equal probability) of being chosen. This also means that for a random sample of size n, every member of the population has an equal chance of being chosen. Otherwise, the sample is a non-random sample. 2 Estimation Actual population mean:  Actual population variance: 2 Sample mean: x Sample variance (no notation) Unbiased estimate for population mean: x Unbiased estimate for population variance: 2s 2 sample variance1 ns n= − If Σx and Σx2 are given: xx n= ( ) 2 22 1 1 x sx nn  =− −   (in MF27) If Σ(x – c) and Σ(x – c)2 are given: ( )xcxc n −=+ ( ) ( )( ) 2 22 1 1 xc s x c nn  −= − −−   If ( ) 2 xx− is given: ( ) 2 2 1 xxns nn  −= −   (in MF27) 3 Sampling Distribution Normal Population Non-Normal/Unknown distribution Population Known population variance 2 2 ~ N ,X n   and ( ) 2 12 ... ~ N ,nX X X n n + + + for any sample size n 2 ~ N ,X n   approx. and ( ) 2 12 ... ~ N ,nX X X n n + + + approx. by Central Limit Theorem where 30n Unknown population variance 2 ~ N , sX n  approx. where n is large* *In our syllabus, if the population variance is unknown, the sample size n will be large. 2 ~ N , sX n  approx. by Central Limit Theorem where 30n