The assumed mean is 47 not 37 so please resolve it

Question

ScanSolve AI Tutor · Accepted Answer

Okay, let's recalculate the mean using an assumed mean of 47.

First, let's update the table with the new assumed mean $A = 47$ :

Age Group	Frequency ( $f$ )	Class Midpoint ( $x$ )	Cumulative Frequency ( $cf$ )	Deviation ( $d = x - 47$ )	$fd$
10-19	6	14.5	6	-32.5	-195
20-29	12	24.5	18	-22.5	-270
30-39	15	34.5	33	-12.5	-187.5
40-49	9	44.5	42	-2.5	-22.5
50-59	5	54.5	47	7.5	37.5
60-69	2	64.5	49	17.5	35
Total	$\sum f = 49$				$\sum fd = -602.5$

1) Calculate the mean using an assumed mean of 47.

Identify the assumed mean ( $A$ ), sum of frequencies ( $\sum f$ ), and sum of $fd$ ( $\sum fd$ ).
Given assumed mean $A = 47$ .
From the updated table, $\sum f = 49$ and $\sum fd = -602.5$ .
Apply the formula for the mean using an assumed mean.
$\bar{x} = A + \frac{\sum fd}{\sum f}$
Substitute the values into the formula and calculate.
$\bar{x} = 47 + \frac{-602.5}{49}$ $\bar{x} = 47 - 12.30$ $\bar{x} = 34.70$
The mean using an assumed mean of 47 is $\boxed{\text{34.70}}$ .

Answer