To calculate the standard deviation of the data set 4, 9, 5, 5, 4, 5, we first need to find the mean (average) of the data.
1. **Calculate the Mean:**
Sum of the data = 4 + 9 + 5 + 5 + 4 + 5 = 32
Number of data points = 6
Mean = Sum / Number of data points = 32 / 6 = 5.33 (approx)
2. **Calculate the Variance:**
Variance is the average of the squared differences from the Mean.
– (4 – 5.33)² = 1.77
– (9 – 5.33)² = 13.49
– (5 – 5.33)² = 0.11
– (5 – 5.33)² = 0.11
– (4 – 5.33)² = 1.77
– (5 – 5.33)² = 0.11
Sum of squared differences = 1.77 + 13.49 + 0.11 + 0.11 + 1.77 + 0.11 = 17.36
Variance = Sum of squared differences / Number of data points = 17.36 / 6 = 2.89 (approx)
3. **Calculate the Standard Deviation:**
Standard Deviation = √Variance = √2.89 ≈ 1.70 (approx)
So, the standard deviation of the data set 4, 9, 5, 5, 4, 5 is approximately 1.70.