Respuesta :
→The Data Provided to calculate range is : 3930,4070, 3500, 3200, 2950, 3840, 4070 4060.
→Arranging the data in Ascending order
2950, 3200, 3500, 3840, 3930,4060,4070,4070
1. Now, Range = Maximum Number (in Data Set) - Minimum Number (in Data set)
= 4070 - 2950
= 1120
2. Standard Deviation
Mean = [tex]\frac{\text{Sum of Total number of Observation}}{\text{Total number of observation}}[/tex]
So, Mean of the above data set= [tex]\frac{ 3930 + 4070 + 3500 + 3200 +2950+3840 + 4070 + 4060}{8}=3695[/tex]
Square of Difference between Mean and each value in Data set:
1. (2950 - 3695)²=(-745)²= 555025
2. (3200 - 3695)²= (-495)²=245025
3.(3500 -3695)²= (-195)²= 38025
4. (3840 - 3695)²= (145)²=21025
5. (3930- 3695)²= (235)²=55225
6. (4060 - 3695)²=(365)²=133225
7. (4070 - 3695)²= (375)²=140625
8. (4070 - 3695)²= (375)²=140625
Sum= 555025 +245025+ 38025+21025+55225+133225+140625+140625= 1328800
Standard Deviation= [tex]\sqrt{\frac{1328800}{8}}=\sqrt{166100}[/tex]
= 407.55(approx)
The range for the strength of the concrete is 1120.
The standard deviation for the strength of the concrete is 407.55 psi.
Given
3920, 4070, 3500, 3200, 2950, 3840, 4070, 4060.
What is the range?
The range is defined as the difference between the minimum value and maximum value of the data set.
Arranging the data in Ascending order
2950, 3200, 3500, 3840, 3930,4060,4070,4070
1. The range of the strength of the concrete is;
Range = Maximum number - Minimum number
Range = 4070 - 2950
Range = 1120
2. The mean of the given data set is;
[tex]\rm Mean = \dfrac{2950+3200+3500+3840+ 3930+4060+4070+4070}{8}\\\\Mean =3695[/tex]
The Square of Difference between Mean and each value in Data set:
1. (2950 - 3695)²=(-745)²= 555025
2. (3200 - 3695)²= (-495)²=245025
3.(3500 -3695)²= (-195)²= 38025
4. (3840 - 3695)²= (145)²=21025
5. (3930- 3695)²= (235)²=55225
6. (4060 - 3695)²=(365)²=133225
7. (4070 - 3695)²= (375)²=140625
8. (4070 - 3695)²= (375)²=140625
Therefore,
Add the above results together;
Sum=555025+245025+38025+21025+55225+133225+140625+140625= 1328800
[tex]\rm Standard \ deviation=\sqrt{\dfrac{1328800}{8}}\\\\ Standard \ deviation=\sqrt{166100} \\\\ Standard \ deviation= 407.55[/tex]
Hence, the standard deviation for the strength of the concrete is 407.55 psi.
To learn more about Range click the link given below.
https://brainly.com/question/8041076
