Use the table to answer the question.

Question

Find the standard deviation of the data set, rounded to the nearest hundredth.

(2 points)
Data Point 15 18 11 17 14
Difference
3
2 −1
Squared 0 9
4 1

Answer 1

To find the standard deviation of the data set, we need to follow these steps:

1. Calculate the Mean:

   • Data Points: 15, 18, 11, 17, 14
   • Mean = (15 + 18 + 11 + 17 + 14) / 5 = 75 / 5 = 15

2. Find the Differences from the Mean:

   • Differences:
     • 15 - 15 = 0
     • 18 - 15 = 3
     • 11 - 15 = -4
     • 17 - 15 = 2
     • 14 - 15 = -1

3. Square the Differences:

   • Squared Differences:
     • 0² = 0
     • 3² = 9
     • (-4)² = 16
     • 2² = 4
     • (-1)² = 1

4. Calculate the Variance:

   • Variance = (Sum of Squared Differences) / (Number of Data Points)
   • Variance = (0 + 9 + 16 + 4 + 1) / 5
   • Variance = 30 / 5 = 6

5. Calculate the Standard Deviation:

   • Standard Deviation = √Variance
   • Standard Deviation = √6 ≈ 2.45 (rounded to the nearest hundredth)

Therefore, the standard deviation of the data set is approximately 2.45.