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 year's results were: Aptitude Score 0 1 2 3 4 5 Frequency 7 4 2 5 3 3i) The mean aptitude score is: ii) The median aptitude score is: _.

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dfbustos dfbustos · Answer 1 · 2020-03-10T01:26:46+01:00

Answer:

i) [tex] \bar X = \frac{\sum_{i=1}^n X_i f_i}{\sum_{i=1}^n f_i}[/tex]

And replacing we got:

[tex] \bar X = \frac{0*7 + 1*4 + 2*2 + 3*5 + 4*3 + 5*3}{7+4+2+5+3+3}= \frac{50}{24}= 2.083[/tex]

ii) For this case we have a total of 24 values and we can calculate the median from the grouped data so we have the following values:

0,0,0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,3,4,4,4,5,5,5

And we can calculate the median from the position 12 and 13 from the data ordered and we got:

[tex] Median = \frac{2+2}{2}= 2[/tex]

Step-by-step explanation:

For this case we have the following data:

Aptitude Frequency

0 7

1 4

2 2

3 5

4 3

5 3

Part i

For this case we can calculate the mean with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i f_i}{\sum_{i=1}^n f_i}[/tex]

And replacing we got:

[tex] \bar X = \frac{0*7 + 1*4 + 2*2 + 3*5 + 4*3 + 5*3}{7+4+2+5+3+3}= \frac{50}{24}= 2.083[/tex]

Part ii

For this case we have a total of 24 values and we can calculate the median from the grouped data so we have the following values:

0,0,0,0,0,0,0,1,1,1,1,2,2,3,3,3,3,3,4,4,4,5,5,5

And we can calculate the median from the position 12 and 13 from the data ordered and we got:

[tex] Median = \frac{2+2}{2}= 2[/tex]