Measures of Position : Statistic

स्थिति सूचक मान 

Like us on Facebook https://www.facebook.com/focussgurgaon

Measures of position are techniques that divide a set of data into equal groups.

To determine the measurement of position, the data must be sorted from lowest to highest. The different measures of position are:

• Quartiles (चतुर्थांक )
• Deciles(दशांक )
• Percentiles(प्रतिशतांक )

Quartiles

The quartiles are the three values of the variable that divide an ordered data set into four equal parts.

Q₁, Q₂ and Q₃ determine the values for 25%, 50% and 75% of the data.

Q₂ coincides with the median.

Determining Quartiles

1. Order the data from smallest to largest.

2. Find the place that occupies every quartile using the expression , in the cumulative frequency tables.

Odd Number of Data

2, 5, 3, 6, 7, 4, 9

Even Number of Data

2, 5, 3, 4, 6, 7, 1, 9

Calculation of Quatiles for Grouped Data

L_i is the lower limit of the quartile class.

N is the sum of the absolute frequency.

F_i-1 is the absolute frequency immediately below the quartile class.

a_i is the width of the class containing the quartile.

The quartiles are independent of the widths of the classes.

Deciles

The deciles are the nine values of the variable that divide an ordered data set into ten equal parts.

The deciles determine the values for 10%, 20%... and 90% of the data.

D₅ coincides with the median.

Calculating Deciles

1. Order the data from smallest to largest.

2. Find the place that occupies every decile using the expression , in the cumulative frequency table.

L_i is the lower limit of the decile class.

N is the sum of the absolute frequency.

F_i-1 is the absolute frequency immediately below the decile class.

a_i is the width of the class containing the decile class.

The deciles are independent of the widths of the classes.

Percentiles

The percentiles are the 99 values of the variable that divide an ordered data set into 100 equal parts.

The percentiles determine the values for 1%, 2%... and 99% of the data.

P₅₀ coincides with the median.

Determining Percentiles

1. Order the data from smallest to largest.

2. Find the place that occupies every percentile using the expression , in the cumulative frequency table.

L_i is the lower limit of the percentile class.

N is the sum of the absolute frequency.

F_i-1 is the absolute frequency immediately below the percentile class.

a_i is the width of the class containing the percentile.

The percentiles are independent of the widths of the classes.