The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
<h3>How to determine the mean?</h3>
The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
![\bar x = \frac{\sum fx}{\sum f}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20fx%7D%7B%5Csum%20f%7D)
So, we have:
![\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B99.5%2A%20345%20%2B%20299.5%2A%2097%20%2B%20499.5%2A%2052%20%2B%20699.5%20%2A%2021%20%2B%20899.5%20%2A%209%20%2B%20%201099.5%20%2A%208%20%2B%201299.5%20%2A%203%7D%7B345%20%2B%2097%20%2B%2052%20%2B%2021%20%2B%209%20%2B%208%20%2B3%7D)
Evaluate
![\bar x = 233.331775701](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20233.331775701)
Approximate
![\bar x = 233.3](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20233.3)
Hence, the approximation of the mean is 233.3
<h3>How to determine the standard deviation?</h3>
The standard deviation is calculated as:
![\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%20f%28x%20-%20%5Cbar%20x%29%5E2%7D%7B%5Csum%20f%7D%7D)
So, we have:
![\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}](https://tex.z-dn.net/?f=%5Csigma%3D%20%5Csqrt%7B%5Cfrac%7B%2899.5-233.3%29%5E2%2A%20345%20%2B%20%28299.5-233.3%29%5E2%2A%2097%20%2B......%20%2B%20%281299.5%20-233.3%29%5E2%2A%203%7D%7B345%20%2B%2097%20%2B%2052%20%2B%2021%20%2B%209%20%2B%208%20%2B3%7D)
Evaluate
![\sigma = 229.82](https://tex.z-dn.net/?f=%5Csigma%20%3D%20229.82)
Hence, the approximation of the standard deviation is 229.82
Read more about mean and standard deviation at:
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Find volume
vcube=side^3
side=2
vcube=2^3=8cm^3
19 grams per cm^3
19 times 8=152 grams
Answer:
B
Step-by-step explanation:
25 x 4 = 100
17 x 4 = 68
B = 68