By going through these Maharashtra State Board Class 11 Economics Notes Chapter 3 Partition Values students can recall all the concepts quickly.

## Maharashtra State Board Class 11 Economics Notes Chapter 1 Basic Concepts in Economics

→ **Types Of Averages:**

(1) Arithmetic Mean ( \(\bar{x}\) ):

- Individual Data

\(\bar{x}=\frac{\sum x}{n}\) - Discrete Series / Data

\(\bar{x}=\frac{\sum f_{i} x_{i}}{n}\) - Continuous Series / Data Direct Method

\(\bar{x}=\frac{\sum f_{i} x_{i}}{n}\)

(2) Mode (Z):

- Individual Data

Maximum Repeated value - Discrete Series/ Data

Maximum Frequency Value - Continuous Series / Data

\(\mathrm{Z}=l+\left[\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\right] \times h\)

(3) Median (M) :

- Individual Data

M = Size of \(\left(\frac{n+1}{2}\right)^{\text {th observation }}\) - Discrete Series I Data

M = Size of \(\left(\frac{n+1}{2}\right)^{\text {th observation }}\) - Continuous Series I Data

M = \(l\left(\frac{\frac{n}{2}-c . f .}{f}\right) \times h\)

→ 29th June is celebrated as “Statistics Day” in India to recognise the contributions of noted Indian

Statistician. Prof. Prasanta Chandra Mahalanobis.

→** Partition Values :** Values which divide the data into required number of equal parts are called partition value or fractiles.

**→ Partition Values:**

- Percentiles
- Quartiles
- Median
- Deciles

→** Application Of Partition Value:**

- Quartiles
- Deciles
- Percentiles

Quartiles:

- Used in study of Financial Information
- E.g.
- Economic Data
- Income Data
- Stock Data
- Sales
- Survey Data, etc

Deciles:

Used in Finance and Economics

Used to Study:

- Level of economic
- Inequality
- Measurement of poverty line
- Drought cohdition, etc.

Percentiles:

Used in Measurement of test scores, health indication, household income, household wealth, etc.

→** Quartiles :** Quartiles are the values (data) which divide the series (distribution) into four equal parts. They are the 3 values that divide the distribution into 4 parts, each representing one quarters of the score. These 3 values are called as first quartile (Q_{1}), second quartile (Q_{2}) and third quartile (Q_{3}). Second quartile is nothing but the median.

**→ Quartiles**

**Q _{1} Individual Data:**

Q

_{1}= size of \(\left(\frac{n+1}{4}\right)^{\text {th observation }}\)

Discrete Data:

Q_{1} = size of \(\left(\frac{n+1}{4}\right)^{\text {th observation }}\)

Continuous Data (Grouped Data):

Step:

- Q
_{1}= size of \(\left(\frac{n}{4}\right)^{\text {th observation }}\) - Q
_{1}= l + \(\left(\frac{\frac{n}{4}-c f}{f}\right)\) x h

**Q _{2} Median Individual Data:**

Q

_{2}= size of \(\left(\frac{n+1}{4}\right)^{\text {th observation }}\)

= size of \(\left(\frac{n+1}{2}\right)^{\text {th observation }}\)

Discrete Data :

Q_{2} = size of \(\left(\frac{n+1}{2}\right)^{\text {th observation }}\)

Continuous Data (Grouped Data):

Step:

- Q
_{2}= size of \(\left(\frac{2n}{4}\right)^{\text {th observation }}\) - Q
_{2}= l + \(\left(\frac{\frac{2 n}{4}-c f}{f}\right)\) x h

[Note : Q_{2}= D_{5}= P_{50}Median]

**Q _{3 }Individual Data:**

Q

_{3}= size of 3\(\left(\frac{n+1}{4}\right)^{\text {th observation }}\)

Discrete Data:

Q_{3} = size of 3\(\left(\frac{n+1}{4}\right)^{\text {th observation }}\)

Continuous Data (Grouped Data):

Step:

- Q
_{3}= size of \(\left(\frac{3 n}{4}\right)^{\text {th } \text { Observation }}\) - Q
_{3}= l + \(\left(\frac{\frac{3 n}{4}-c f}{f}\right)\) x h

→** Deciles :** They are the values of data which divide the whole set of observations into 10 equal parts. There are 9 points i.e. , D_{1}, D_{2} to D_{9} which divide the data into 10 equal parts. While calculating Deciles, data has to be arranged in ascending or descending order.

- Individual Data : \(\mathrm{D}_{j}=j\left(\frac{n+1}{10}\right)^{\text {th } \text { Observation }}\) [where j = 1,2, ……..9]
- Continuous Data : \(\mathrm{D}_{j}=l+\left(\frac{\frac{j n}{10}-c f}{f}\right) \times h\) [where j = 1,2, ………….9]

→ **Percentiles :** It divides the whole set of observations into 100 equal parts. There are 99 percentile.

They are denoted by P_{1}, P_{2} to P_{3} ………….. P_{99} The 50th percentile is called as Median.

(i) Individual Data and Discrete Data : P_{k} = size of k \(\left(\frac{n+1}{100}\right)^{\text {th observation }}\) [Where k = 1, 2, ……………99]

(ii) Continuous Data : P_{k} = l + \(\left(\frac{\frac{k n}{100}-c f}{f}\right)\) x h [Where k = 1, 2, ……………99]

**Word Meaning:**

procedure – steps; arithmetic – study of numbers; mean – average; median – middle; quartiles – divided into four equal groups; deciles – divided into 10 equal groups; percentiles – divided into 100 equal groups; descriptive – to describe; poverty – poor; acquainted – to get to known; statistical – use of statistics; magnitude – in great extent; misinterprets – misunderstand; survey – observe; fluctuations – changes; inflation – increase in price; povertyline – minimum required income to get basic needs of life; drought – no rainfall in an area; portfolio investments – range of investments; bench marking – measuring the performance; baseline – minimum way tci compare; observations – the data in numbers; frequency distribution – mathematical function; symbolically – representating in terms; cumulative – increased in quantity by adding one after other continuously.