Find the standard deviation of 2 3 8 10 and 12 - JAMB Mathematics 2024 Question

To find the standard deviation, we follow these steps:

1. Find the mean of the data: The data set is: 2, 3, 8, 10, 12.
2. Find the squared differences from the mean for each data point:
   • For 2: \( (2 - 7)^2 = (-5)^2 = 25 \)
   • For 3: \( (3 - 7)^2 = (-4)^2 = 16 \)
   • For 8: \( (8 - 7)^2 = (1)^2 = 1 \)
   • For 10: \( (10 - 7)^2 = (3)^2 = 9 \)
   • For 12: \( (12 - 7)^2 = (5)^2 = 25 \)
3. Find the variance: The variance \( \sigma^2 \) is the average of the squared differences:
4. Find the standard deviation: The standard deviation \( \sigma \) is the square root of the variance:

S.D = \(\sqrt{\frac{(x - \varkappa)^2}{n}}\)

S.D = \(\sqrt{\frac{76}{5}}\)

S.D = 3.9

Therefore, the standard deviation is approximately 3.9.