Question

class midpoints, x|frequence, f|xf
170.5|3
172.5|2
174.5|5
176.5|6
178.5|7
180.2|4
182.5|3
find the estimated mean. for the table above

Explanation:

Step1: Calculate xf for each row

For the first row: $170.5\times3 = 511.5$
For the second row: $172.5\times2=345$
For the third row: $174.5\times5 = 872.5$
For the fourth row: $176.5\times6=1059$
For the fifth row: $178.5\times7 = 1249.5$
For the sixth row: $180.5\times4=722$
For the seventh row: $182.5\times3 = 547.5$

Step2: Calculate the sum of f

$\sum f=3 + 2+5+6+7+4+3=30$

Step3: Calculate the sum of xf

$\sum xf=511.5+345 + 872.5+1059+1249.5+722+547.5=5307$

Step4: Calculate the estimated mean

The formula for the estimated mean $\bar{x}=\frac{\sum xf}{\sum f}$
$\bar{x}=\frac{5307}{30}=176.9$

Answer:

$176.9$