In Genesis 50:22 the text literally says:
וַיְחִ֣י יוֹסֵ֔ף מֵאָ֥ה וָעֶ֖שֶׂר שָׁנִֽים1
"Joseph lived a hundred and ten years"
In v. 26, an idiomatic expression is used to say the same thing. The text of Genesis 50:26 literally says:
בֶּן־מֵאָ֥ה וָעֶ֖שֶׂר שָׁנִ֑ים2
"son of a hundred and ten years"
This is a common idiom used for expressing age in Biblical Hebrew.3 Neither expression indicates a difference in how the age should be calculated (and I cannot find any support for different calculations in scholarly literature).
The IVP Commentary offers the following information:
Joseph dies at the age of 110, considered the ideal age for an
Egyptian. Examination of mummies has demonstrated that the average
life expectancy in Egypt was between forty and fifty years. The use of
the coffin or sarcophagus in mummification was an Egyptian, not an
Several sources corroborate that 110 years of age was an ideal age of death for Egyptians.5 Overall, this information is likely repeated because it demonstrates that Joseph was a successful Egyptian official, and his age of death was a cultural confirmation of this that would have been understood by the original readers.
The context of this passage affirms that Joseph was a Hebrew, not an Egyptian, and yet emphasizes his success in both cultures. His burial was finally with the Hebrews and according to Hebrew customs rather than Egyptian practices (embalming and burial vs. mummifying).6
1 Biblia Hebraica Stuttgartensia: SESB Version., electronic ed. (Stuttgart: German Bible Society, 2003), Ge 50:22.
2 Ibid., Ge 50:26.
3 Lexical entry for בֵּן: "in expressions specifying age (→ בַּת 4): aged (so much) (MHb. JArm. Palm. Syr. Arb. Soq.): בֶּן־שְׁמֹנַת יָמִים eight days old Gn 1712, בֶּן־שָׁנָה one year old Ex 125 (1S 131 the number is missing), בֶּן־שְׁנָתוֹ (“situation specification” Landsberger JNES 8:288, → יוֹם 3, חֹדֶשׁ 2, BL 5181) one year old Lv 2312 (6 ×), בֶּן־חֲמֵשׁ מֵאוֹת שָׁנָה Gn 532, בִּן־לַיְלָה one night old, meaning grown up in one night Jon 410...."
Ludwig Koehler et al., The Hebrew and Aramaic Lexicon of the Old Testament (Leiden; New York: E.J. Brill, 1999), 138.
4 Victor Harold Matthews, Mark W. Chavalas, and John H. Walton, The IVP Bible Background Commentary: Old Testament, electronic ed. (Downers Grove, IL: InterVarsity Press, 2000), Ge 50:26.
5 Marie Parsons. "Old Age in Ancient Egypt." (Tour Egypt), retrieved from the Tour Egypt website. A search for this information will reveal numerous sources showing that 110 years was an ideal age of death for Egyptians.
6 James McKeown. Genesis: Two Horizons Old Testament Commentary series. (Grand Rapids, MI: Wm. B. Eerdmans Publishing Co., 2008), 192-193.