1.what is the interquartile range for the data set?
89, 91, 95, 112, 118, 83, 85, 104, 118, 125, 134, 138

2.what is the standard deviation for the data set? 212, 249, 212, 248, 239, 212, 216, 234, 248

1. First, put the range in order and then divide the set into quarters. In this case, quartiles are between numbers.
83, 85, 89,   l    91, 95, 104,  l   112, 118, 118,  l  125, 134, 138
Q₁ = (89 + 91)/2 = 90
Q₂ = (104 + 112)/2 =108
Q₃ = (118 + 125)/2 = 121.5
Interquartile range (IQR) = Q₃ - Q₁
                                        = 121.5 - 90
                                 IQR = 31.5
2. To find the standard deviation follow the simple steps.
Formula in finding the standard deviation: (see attached file)
     Step 1. Work out the simple average of the numbers (mean)
                212 + 249 + 212 + 248 + 239 + 212 + 216 + 234 + 248
                                                 9
              = 2070
                     9
mean (μ) = 230
    
    Step 2. Subtract the mean on each number and square the result.
212 - 230 = (-18)² = 324
249 - 230 = ( 19)² = 361
212 - 230 = (-18)² = 324
248 - 230 = (18)²  = 324
239 - 230 = (9)²    = 81
212 - 230 = (-18)² =324
216 - 230 = (-14)² =196
234 - 230 = (4)²    =16
248 - 230 = (18)²  =324

     Step 3. Add all the squared results and get the mean.
                  2274
                     9
       Variance = 252.6666667
    Step 4. Get the square root of the variance.
                  √252.6666667
                  = 15.89549202
     

It’s b because vpt is the whole triangle and ptc isn’t