Business statistics

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Percentiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Percentiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Percentiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Percentiles

• As another illustration of this procedure, let us consider the calculation of the 50th percentile for the starting salary data. Applying step 2, we obtain
• Because i is an integer, step 3(b) states that the 50th percentile is the average of the sixth and seventh data values; thus the 50th percentile is (3490 + 3520)/2 = 3505.
• Note that the 50th percentile is also the median.

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

It is often desirable to divide data into four parts, with each part containing approximately one-fourth, or 25% of the observations. Figure 3.1 shows a data distribution divided into four parts. The division points are referred to as the quartiles and are defined as

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Example 2.

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Example 2.

Step 1. Arrange the data in ascending order as following:

105 135 180 210 245 250 265 380 395 420 430 615 690 830 1180

n = 15

Step 2. Compute Q1 and Q3

• Q1 = = (25/100)x15 = 3.75 (not integer) 4 = 210 minutes
• Q3 = (75/100)x15 = 11.25 (not integer) 12 = 615 minutes

Chapter 3. Descriptive Statistics: Numerical Measures

3.1. Measures of Location

Quartiles

Example 2.

Step 3. Compute Q2

Q2 = (50/100)x15 = 7.5 (not integer) 8 (median) = 380 minutes

25% 25% 25% 25%

105 135 180 210 245 250 265 380 395 420 430 615 690 830 1180

Q1 = 210 Q2 = 380 Q3 = 615