Question

every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). this years results were:
the average (mean) aptitude score:
the median aptitude score:
question help: video 1 video 2

Explanation:

Step1: Calculate the total number of students

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Step2: Calculate the sum of (score \(\times\) frequency)

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Step3: Calculate the mean

The mean formula is \(\bar{x}=\frac{\sum_{i = 0}^{5}(x_i\times f_i)}{n}\). Substitute \(\sum_{i = 0}^{5}(x_i\times f_i) = 58\) and \(n = 22\) into the formula:

$$ \bar{x}=\frac{58}{22}\approx2.6 $$

Step4: Calculate the median

Arrange the data in ascending order. The cumulative - frequency:

• For score \(0\): cumulative frequency \(CF_0=3\)
• For score \(1\): cumulative frequency \(CF_1=3 + 4=7\)
• For score \(2\): cumulative frequency \(CF_2=7+4 = 11\)
• For score \(3\): cumulative frequency \(CF_3=11 + 3=14\)
• For score \(4\): cumulative frequency \(CF_4=14+3 = 17\)
• For score \(5\): cumulative frequency \(CF_5=17+5 = 22\)

Since \(n = 22\) (even), the median is the average of the \(\frac{n}{2}=11\)th and \((\frac{n}{2}+1)=12\)th values. The \(11\)th and \(12\)th values fall in the score \(2\) category. So the median is \(2\).

Answer:

The average (mean) aptitude score: \(2.6\)
The median aptitude score: \(2\)