What do you mean by partition values? In what respect they are different from

median? Explain any three partition values with their formulas.

Ans Partition Values:

Partition values are points that divide a dataset into specific portions or intervals. These

values are used in various statistical measures to understand the distribution of data.

Unlike the median, which is a specific partition value representing the middle point of a

dataset, other partition values can be used to divide the data in different ways.

Difference from Median:

The median is a particular partition value that separates the dataset into two equal halves,

with 50% of the values falling below it and 50% above it. In contrast, other partition values

can divide the data into different proportions or intervals.

Three Partition Values with Formulas:

- Quartiles:

Quartiles are three partition values that divide a dataset into four equal

parts. The three quartiles are denoted as Q1, Q2, and Q3.

Formulas:

Q1Q1: The value below which 25% of the data falls.

Q1=Median of the lower half of the datasetQ1=Median of the lower

half of the dataset

Q2Q2: The median, separating the lower and upper halves of the

dataset.

Q3Q3: The value below which 75% of the data falls.

Q3=Median of the upper half of the datasetQ3=Median of the upper

half of the dataset - Deciles:

Deciles are nine partition values that divide a dataset into ten equal parts.

The three quartiles can be considered as specific deciles (Q1 is the first

decile, Q2 is the fifth decile or median, and Q3 is the ninth decile).

Formulas: Dk Dk: The kth decile is the value below which k1010k of the data

falls. Dk=Median of the subset of data below the (k/10)-th position Dk=Median of the subset of data below the (k/10)-th position - Percentiles:

Percentiles are 99 partition values that divide a dataset into 100 equal parts.

The three quartiles and nine deciles can be considered specific percentiles

(Q1 is the 25th percentile, Q2 is the 50th percentile, and so on).

Formula:

PpPp: The pth percentile is the value below which p%p% of the data

falls. Pp=Median of the subset of data below the (p/100)-th position Pp=Median of the subset of data below the (p/100)-th position. These partition values provide insights into the spread and distribution of data. Quartiles, deciles, and percentiles are particularly useful when analyzing datasets that may not have a symmetrical or normal distribution, allowing researchers to understand the distribution of values across different percentiles or intervals.