Question

What is the standard deviation of the data set?. 14 34 23 50 25 16 48. . a. about 35.6. . b. about 26.8. . c. about 14.5. . d. about 13.4. my answer: c. about 14.5. or is it d?? idk please help i got confused... on the scientific calculator, is Sx the symbol for standard deviation? or is it something else?.

Answer 1

The standard deviation of the data set is D. ABOUT 13.4

14, 34, 23, 50, 25, 16, 48

Arrange in ascending order: 14, 16, 23, 25, 34, 48, 50

mean = (14 + 16 + 23 + 25 + 34 + 48 + 50) / 7 = 210/7 = 30

|14 - 30| = 16 ⇒ 16² = 256
|16 - 30| = 14 ⇒ 14² = 196
|23 - 30| = 7 ⇒ 7² = 49
|25 - 30| = 5 ⇒ 5² = 25
|34 - 30| = 4 ⇒ 4² = 16
|48 - 30| = 18 ⇒ 18² = 324
|50 - 30| = 20 ⇒ 20² = 400

(256 + 196 + 49 + 25 + 16 + 324 + 400) / 7 = 1,266/7 = 180.85 variance
√180.85 = 13.45 standard deviation.