MMW W8

1. quartiles

2. deciles

3. percentiles

Measures of Position

Z-score

Measure of relative position

Measures of Position

• Measures of position indicate where a score stands relative to others in a data set.

• They determine if a value is about average or unusually high or low.

• Used for quantitative data on a numerical scale.

• Applicable to ordinal variables.

• Methods:

  • General Method

  • Linear Interpolation

  • Mendenhall and Sincich Method

Quartiles of Ungrouped Data

• Are divide a distribution into four equal parts.

• Q1​: 25% of the data falls below the first quartile.

• Q2​: Median, 50% of the data falls below the second quartile.

• Q3​: 75% of the data falls below the third quartile.

• Interquartile Range: Difference between Q3​ and Q1​.

Deciles of Ungrouped Data

• divide a distribution into ten equal parts.

• Formula: Dk​=(k∗n)/10

• If the result is not a whole number, round up to the next whole number.

• If it is a whole number, use the average of that value and the next.

Percentiles of Ungrouped Data

• Percentiles divide a distribution into one hundred equal parts.

• Formula: Pk​=(k∗n)/100

• If the result is not a whole number, round up to the next whole number.

• If it is a whole number, use the average of that value and the next.

Percentile rank

Indicates the percentage of values below a given value.

• Formula: Percentile rank of x=((number of values below x)+0.5)/n∗10

Measures of Relative Position

• Z score measures

• the distance between an observation and the mean in standard deviation units.

• Formula:

  • Population: zx​=(x−μ)/σ

  • Sample: zx​=(x−xˉ)/s

• If the is positive, the value is above the mean.

• If the is 0, the value equals the mean.

• If the  is negative, the value is below the mean.