The　sample　mean　and　sample　variance　are　commonly　used　statistics　in　our　study.　In　this　paper,　distributions　of　the　sample　mean　and　sample　variance　from　a　skew　normal　population　are　derived　under　closed　skew　normal　(CSN)　settings.　The　noncentral　closed　skew　chi-square　distribution　is　defined,　and　the　distribution　of　quadratic　forms　is　discussed.　Our　results　generalize　the　corresponding　results　given　under　skew　normal　settings.　Several　examples　are　given　for　illustration　of　our　results.　©　2019　Walter　de　Gruyter　GmbH,　Berlin/Boston.