find the mean of the data summarized in the given frequency distribution. compare the computed mean to the…

find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 51.4 miles per hour.\nspeed (miles per hour) | 42 - 45 | 46 - 49 | 50 - 53 | 54 - 57 | 58 - 61\nfrequency | 21 | 13 | 7 | 4 | 2\nthe mean of the frequency distribution is miles per hour.\n(type an integer or decimal rounded to one decimal place as needed.)

find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 51.4 miles per hour.\nspeed (miles per hour) | 42 - 45 | 46 - 49 | 50 - 53 | 54 - 57 | 58 - 61\nfrequency | 21 | 13 | 7 | 4 | 2\nthe mean of the frequency distribution is miles per hour.\n(type an integer or decimal rounded to one decimal place as needed.)

Answer

Explanation:

Step1: Find mid - points

For the interval $42 - 45$, mid - point $x_1=\frac{42 + 45}{2}=43.5$; for $46 - 49$, $x_2=\frac{46+49}{2}=47.5$; for $50 - 53$, $x_3=\frac{50 + 53}{2}=51.5$; for $54 - 57$, $x_4=\frac{54+57}{2}=55.5$; for $58 - 61$, $x_5=\frac{58 + 61}{2}=59.5$.

Step2: Calculate the product of mid - points and frequencies

$f_1 = 21$, $f_1x_1=21\times43.5 = 913.5$; $f_2 = 13$, $f_2x_2=13\times47.5 = 617.5$; $f_3 = 7$, $f_3x_3=7\times51.5 = 360.5$; $f_4 = 4$, $f_4x_4=4\times55.5 = 222$; $f_5 = 2$, $f_5x_5=2\times59.5 = 119$.

Step3: Calculate the sum of frequencies and the sum of products

$\sum f_i=21 + 13+7 + 4+2=47$; $\sum f_ix_i=913.5+617.5 + 360.5+222+119 = 2232.5$.

Step4: Calculate the mean

The mean $\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{2232.5}{47}\approx47.5$.

Answer:

$47.5$