Respuesta :
Answer:
[tex]\bar X = \frac{2276}{48}=47.417[/tex]
If we compare this value with the 47.3 proposed we have the following error
[tex] Error = \frac{|Actual-real|}{real}*100 = \frac{|47.417-47.3|}{47.3}*100 =0.247\%[/tex]
The computed mean is close to the actual mean because the difference between the means is less than 5%.
Step-by-step explanation:
Assuming the following dataset:
Speed 42-45 46-49 50-53 54-57 58-61
Freq. 21 15 6 4 2
And we are interested in find the mean, since we have grouped data the formula for the mean is given by:
[tex] \bar X = \frac{\sum_{i=1}^n x_i f_i}{\sum_{i=1}^n f_i}[/tex]
And is useful construct a table like this one:
Speed Freq Midpoint Freq*Midpoint
42-45 21 43.5 913.5
46-49 15 47.5 712.5
50-53 6 51.5 309
54-57 4 55.5 222
58-61 2 59.5 119
Total 48 2276
And the mean is given by:
[tex]\bar X = \frac{2276}{48}=47.417[/tex]
If we compare this value with the 47.3 proposed we have the following error
[tex] Error = \frac{|Actual-real|}{real}*100 = \frac{|47.417-47.3|}{47.3}*100 =0.247\%[/tex]
The computed mean is close to the actual mean because the difference between the means is less than 5%.
