Question

2.Find the mean of the frequency table below.DataFrequency91185710113

Answer 1

The mean of a data set is given by the expression

$\operatorname{mean}=\sum ^N_{n\mathop=0}(\frac{1}{N})a_n$

Where N is the number of elements of the data set and a_n the different elements in the data set.

Since some elements are repeated we can reduce the former formula into the next expression:

$\operatorname{mean}=\sum ^M_{m=0}(\frac{1}{N})(k_m)a_m$

Where N is the number of elements in the data set, M is the number of not repeated elements.

Therefore, in the case of our problem:

$\operatorname{mean}=(\frac{1}{N})(9\cdot11+8\cdot5+7\cdot10+11\cdot3)$

We need to identify N and we can do it by adding up the frequencies:

$N=11+5+10+3=29$

Then, the mean is:

$\operatorname{mean}=\frac{1}{29}(242)\approx8.345$