Mathematics: 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.

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Find the mean of the data summarized in the given

Winzen07

14.01.2022

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

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%.

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