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
