Chapter 1: Q 104. (page 73)

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) $(\frac{Q_{1} + Q_{3}}{2})$
(b) $(\frac{m a x - m i n}{2})$

Short Answer

Expert verified

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 $(\frac{\max - \min}{2})$ to measure the resistance.

Step by step solution

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 $\frac{Max - Min}{2}$

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: $\frac{M a x - M i n}{2}$

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, $\frac{M a x - M i n}{2}$ is used to measure resistance.

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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) $(\frac{Q_{1} + Q_{3}}{2})$
(b) $(\frac{m a x - m i n}{2})$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Concept

Part (a) Step 3: Calculation

Part (b) Step 1: Concept

Part (b) Step 1: Calculation

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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) Q1+Q32(b) max-min2

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Concept

Part (a) Step 3: Calculation

Part (b) Step 1: Concept

Part (b) Step 1: Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Logic and Functions

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

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) $(\frac{Q_{1} + Q_{3}}{2})$
(b) $(\frac{m a x - m i n}{2})$