Statistics
Mean and standard deviation equations
nta_pyq_2025_apr
Grade 12
Question:
Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and$\sqrt{2}$respectively. Then the mean deviation about the mode of these observations is :
Step-by-Step Solution
Key Concept: Translate the given mean and standard deviation equations into equations using$$\bar{x}$=$\tfrac{\sum x_i}${n}$and the variance formula.
$24 + a + b = 4$8 (1)$a + b = 8$2 2$4 + 1 + 1 + 0 + 1 + 9 + (a - 4) + (b - 4)$$2 = 8$2 2$16 = 48 + a + b - 8a - 8b$2 2$a + b = 32$$32 = 2ab$$ab = 16$$a = 4b = 4$$mode = 4$$2 + 1 + 1 + 0 + 1 + 3 + 0 + 0$mean deviation = = 1 8 option (1)
Correct Answer: 1