Question

in this problem, im going to use decimal places. every year, the students at a school are given a musical aptitude test (scored from 0 to 5 (with 5 being perfect)). this years results were:

aptitude score	0	1	2	3	4	5
frequency	4	2	3	2	4	7

the average (mean) aptitude score:
the median aptitude score:

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Explanation:

Step1: Calculate the sum of products of score and frequency

The sum of products $\sum_{i = 0}^{5}(x_{i}f_{i})=0\times4 + 1\times2+2\times3 + 3\times2+4\times4+5\times7=0 + 2+6 + 6+16+35 = 65$.

Step2: Calculate the total frequency

The total frequency $N=\sum_{i = 0}^{5}f_{i}=4 + 2+3 + 2+4+7=22$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 0}^{5}(x_{i}f_{i})}{N}=\frac{65}{22}\approx2.95$.

Step4: Find the median position

Since $N = 22$ (an even - numbered data set), the median position is $\frac{N}{2}=11$ and $\frac{N}{2}+1 = 12$.

Step5: Arrange the data in cumulative - frequency form

The cumulative frequencies are: $4$ (for score 0), $4 + 2=6$ (for score 1), $6+3 = 9$ (for score 2), $9+2 = 11$ (for score 3), $11 + 4=15$ (for score 4), $15+7 = 22$ (for score 5). The 11th and 12th ordered values fall into the score of 3. So the median is 3.

Answer:

The mean is approximately $2.95$ and the median is 3.