In drawing histogram for unequal class intervals, the height of... | Agrigyan

Botanical and agronomic crop classification:

• Rice (Oryza sativa) is a major cereal crop belonging to the family Poaceae (Gramineae).
• Wheat (Triticum aestivum) is a principal cereal crop belonging to family Poaceae.
• Gram or chickpea (Cicer arietinum) belongs to the family Fabaceae (Leguminosae) and is classified as a pulse/grain legume, not a cereal.
• Maize (Zea mays) is a staple cereal grain belonging to family Poaceae.

Fundamental algebraic property of arithmetic mean:

• By definition, $\sum_{i=1}^{n} (X_i - \bar{X}) = \sum X_i - n\bar{X} = n\bar{X} - n\bar{X} = 0$. The algebraic sum of deviations about the arithmetic mean is always identically zero.
• It can never be negative.
• It can never be positive.
• It is a finite real quantity ($0$), never infinity.

Calculation using binomial distribution:

• Given $n = 300$, probability of defective $p = 0.03$, and $q = 1 - p = 0.97$. The variance is $\sigma^2 = n p q = 300 \times 0.03 \times 0.97 = 9 \times 0.97 = 8.73$. The standard deviation is $\sigma = \sqrt{8.73} \approx 2.9546$.
• $8.73$ is the variance ($\sigma^2$), not the standard deviation.
• $9$ is the expected value / mean ($n p = 300 \times 0.03 = 9$).
• $3$ is a simple rounding of the root without precision.