Question

Compute the range and sample standard deviation for strength of the concrete (in psi) 3930,4070, 3500, 3200, 2950, 3840, 4070 40/60
the range is 11:20 PSI
(round to one decimal place as needed)

Answer 1

→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 = $\frac{\text{Sum of Total number of Observation}}{\text{Total number of observation}}$

So, Mean of the above data set= $\frac{ 3930 + 4070 + 3500 + 3200 +2950+3840 + 4070 + 4060}{8}=3695$

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= $\sqrt{\frac{1328800}{8}}=\sqrt{166100}$

  = 407.55(approx)