My family is having a debate right now. We all have different levels of Jewish observance. My mom and I attend Chabad services of which a Minyan is very important. My sister attended services today for Sukkot and Shabbat and we did not have a Minyan. I have been saying Mourner's Kaddish for my grandmother (she does not have living children) and I asked about saying the Mourner's Kaddish for her today. I was told that we can't say the Mourner's Kaddish because we don't have a Minyan present. We had 6 men present.
My sister then argued and asked "why do we need 10? We have more than 1. It seems arbitrary to have to require 10."
We searched online and found the significance of the number 10 but that doesn't answer my sisters question. My sister's argument is essentially we are willing and 'able' to do the prayer so why not do it? Wouldn't doing the prayer be better than not doing the prayer regardless of the number present? I understand certain reasons why one doesn't do prayers alone but we are asking in the case of praying in public with more than 1 person but less than 10 present.
The public requirement for certain prayers is based on Vayikra 22:32: "I will be hallowed (ונקדשתי) among the children of Israel". Prayers that specifically sanctify God therefore need to be said among the children of Israel. These prayers include the Mourner's Kaddish. (Also Kedusha, Barchu, and reading torah.)
The definition of "among the children of Israel", a minyan, comes from the incident of the spies described in Bamidbar 14. Specifically in Bamidbar 14:27, the ten spies who gave a bad report are referred to as an "evil congregation" (עֵדָה הָרָעָה). From this we learn that a congregation is at least ten.
For further information and reflections on this concept, see this article.
Phillip your question demonstrates your beautiful respect you had for your grandmother, it was worth asking the question (and reading it ) just to gain that lesson, in a society where youth is glorified & age is grounds for neglect, thank G-d Judaism respects it's elders even more than it's youth (rise before an elder, & mesorah)
To answer your question i have learned from various sources one of them was a speach by Rabbi Dr Akiva Tatz, that when the Rabbi's enact an edict, through homiletic interpretation (D'rush) they are not stating their opinion they are bringing a manifestation of G-d's will down here on earth, clearly G-d wants us to realize there is great power when ten gather to sanctify his name, this powerful Kidush Hashem (sanctification of G-d's holy name, simply can not be accomplished without an 'Eidah' (ten men) as in Bamidbar 14:27, the ten spies who gave a bad report are referred to as an "evil congregation" (עֵדָה)it is also known that this sanctification rectifies the lack of G-d's honor that came about through the sin of the spies, this will not be achieved without Ten. May your grandmothers soul be elevated close to G-d in the eternal bond of life & i hope this information deepens your appreciation for 'Minyan' (praying with ten men) & eases the frustration of not being able to say 'kadish' for her. By the way learning Mishnayos is a tremendous merit for the departed & if you can get others to learn Mishnayos for her that would be an even greater merit for her than you learning Mishnayos on your own. May Hasem bless you with all the best:)