Q 104. - The Practice of Statistics for AP

Question

What do they measure? For each of the following summary statistics, decide (i) whether it could be used to measure center or spread and (ii) whether it is resistant. 

(a) $\left(\frac{Q_1+Q_3}{2}\right)$

(b) $\left(\frac{max-min}{2}\right)$

Step-by-Step Solution

Answer

Part (a) The formula is  $\frac{Q_1+Q_3}{2}$ is a formula to measure the spread of the data.

Part (b) The formula is $\left(\frac{\max -\min }{2}\right)$ to measure the resistance.

Part (a) Step 1: Given information

To measure the spread of the data, the formula is $\frac{Q_1+Q_3}{2}$, and to measure the resistance, the formula is $\frac{Max-\mathrm{Min}}{2}$

Part (a) Step 2: Concept

Formula used: $\frac{Q_1+Q_3}{2}$

Part (a) Step 3: Calculation

Given quartiles characterise a data collection's distribution by splitting it into quarters, similar to how the median divides it in half. As a result, the number $\frac{Q_1+Q_3}{2}$ is utilized to calculate the data spread. Thus, $\frac{Q_1+Q_3}{2}$

used to measure spread of data.

Part (b) Step 1: Concept

Formula used: $\frac{Max-Min}{2}$

Part (b) Step 1: Calculation

Given quartiles divide data into quarters, same to how the median divides it in half, to describe its dispersion. As a result, the resistance formula is used. Thus, $\frac{Max-Min}{2}$ is used to measure resistance.