CBSE Class 10 Statistics and Probability — practice questions — page 3

To find the midpoint between two points $A(x_1, y_1)$ and $B(x_2, y_2)$, we use the Midpoint Formula: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ ### Step 1: Identify the coordinates From the given points $A(2, 4)$ and $B(6, 10)$: - $x_1 = 2, y_1 = 4$ - $x_2 = 6, y_2 = 10$ ### Step 2: Calculate the x-coordinate $$x_M = \frac{2 + 6}{2} = \frac{8}{2} = 4$$ ### Step 3: Calculate the y-coordinate $$y_M = \frac{4 + 10}{2} = \frac{14}{2} = 7$$ ### Conclusion The midpoint is $(4, 7)$. This corresponds to option B.

To find the sum of a set of numbers when the mean and the count are known, we use the fundamental formula for the arithmetic mean: $$\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}$$ ### **Step 1: Identify the given values** * Number of values ($n$) = $5$ * Mean = $12$ ### **Step 2: Rearrange the formula** To isolate the sum, we multiply both sides of the equation by the number of values: $$\text{Sum} = \text{Mean} \times \text{Number of values}$$ ### **Step 3: Calculate the final sum** $$\text{Sum} = 12 \times 5$$ $$\text{Sum} = 60$$ Therefore, the sum of the 5 numbers is **60**.

To find the median of a dataset, the values must first be arranged in ascending or descending order. The median is the central value of the distribution. There are two scenarios based on the number of observations ($n$): 1. **Odd number of values ($n$ is odd):** The median is the single value located at the exact middle position, $\rac{n+1}{2}$. 2. **Even number of values ($n$ is even):** There is no single middle value. Instead, there are two middle values at positions $\rac{n}{2}$ and $\rac{n}{2} + 1$. In this case, the median is calculated as the arithmetic mean (average) of these two middle values. \nFormula for even $n$: $$\ ext{Median} = \rac{\ ext{Value at } (n/2) + \ ext{Value at } (n/2 + 1)}{2}$$ \nTherefore, for an even number of sorted values, the median is the average of the two middle values.