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Statistical Measures of Position, For Qk, N=nk/4, Range= Q3 -Q1, for Dk ,…
Statistical Measures of Position
Quartiles
Quartile Points:
Q1 (First Quartile): 25th percentile, divides the lowest 25% of the data.
Q2 (Second Quartile / Median): 50th percentile, divides the data into two equal halves.
Q3 (Third Quartile): 75th percentile, divides the lowest 75% of the data.
Formula for Quartiles:
Definition: Quartiles divide a data set into four equal parts.
Interquartile Range (IQR):
Uses: Identifying the spread and detecting outliers.
Deciles
Definition: Deciles divide a data set into ten equal parts.
Decile Points:
D1 (First Decile): 10th percentile.
D2 (Second Decile): 20th percentile.
.....
D9 (Ninth Decile): 90th percentile.
Formula for Deciles:
Uses: Provides more granular insights compared to quartiles; often used in income and education analysis.
Percentiles
Definition: Percentiles divide a data set into 100 equal parts.
Percentile Points:
P1 (First Percentile): Lowest 1% of the data.
P50 (50th Percentile / Median): Middle value of the data.
P99 (99th Percentile): Highest 1% of the data.
Formula for Percentiles:
Uses: Common in standardized testing, height/weight comparisons, and medical diagnostics.
For Qk, N=nk/4
Range= Q3 -Q1
for Dk , N= nk/10
Where k is decile number from 1 to 9
For Pk , N= nk/100
where k is percentile number from 1 to 99.