The assumed mean is 47 not 37 so please resolve it
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI 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.
Step 1: 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 $\sum fd = -602.5$.
Step 2: Apply the formula for the mean using an assumed mean.
$$ \bar{x} = A + \frac{\sum fd}{\sum f} $$
Step 3: 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 $\boxed{\text{34.70}}$.
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