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Maths Statistics problem

If the mean of the following frequency distribution is 3.66, find the value of a, and also find the median and mode of the distribution.

x - 1 2 3 4 5 6
f - 3 9 a 11 8 7

I thought of working backwards, by adding all of the frequencies together with a, and dividing them by 6 to get 3.66. I multiplied 3.66 by 6 to get the sum of the frequencies, but if I continued to rearrange to find the value of a, I would have gotten a negative number. Any ideas?

Reply 1

GUMI

why can't the answer be negative...

Reply 2

JustARandomer123

Original post by GUMI

why can't the answer be negative...

I thought that because it's a frequency distribution table, it shows how frequently a certain number is chosen in whatever the context of the question is. I could be wrong, but it doesn't make sense to me to have a negative number of times that something has been picked