Question

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 47.3 miles per hour.

Answer 1

Answer:

$\bar X = \frac{2276}{48}=47.417$

If we compare this value with the 47.3 proposed we have the following error

$Error = \frac{|Actual-real|}{real}*100 = \frac{|47.417-47.3|}{47.3}*100 =0.247\%$

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:

$\bar X = \frac{\sum_{i=1}^n x_i f_i}{\sum_{i=1}^n f_i}$

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:

$\bar X = \frac{2276}{48}=47.417$

If we compare this value with the 47.3 proposed we have the following error

$Error = \frac{|Actual-real|}{real}*100 = \frac{|47.417-47.3|}{47.3}*100 =0.247\%$

The computed mean is close to the actual mean because the difference between the means is less than 5%.