Balbharti Maharashtra State Board Class 11 Economics Important Questions Chapter 3 Partition Values Important Questions and Answers.

## Maharashtra State Board 11th Economics Important Questions Chapter 3 Partition Values

1A. Complete the correlation:

Question 1.

Quartiles : 4 parts : : 10 parts : __________

Answer:

Deciles

Question 2.

10 parts : Deciles : : Percentiles : __________

Answer:

100 parts

Question 3.

Individual Data : __________ : : Discrete Data : \(\bar{x}=\frac{\sum f_{i} x_{i}}{n}\)

Answer:

\(\bar{x}=\frac{\sum x}{n}\)

Question 4.

Q_{2} : Q_{50} : : D_{5} : __________

Answer:

Median

1B. Suggest the economic terms for the given statements:

Question 1.

The value that divides the data into hundred equal parts.

Answer:

Percentiles

Question 2.

Values that divide the data into the required number of equal parts.

Answer:

Partition values or Fractiles

Question 3.

Value of the middlemost observation in the data.

Answer:

Median

Question 4.

Extreme value on the lower side and higher side in magnitude.

Answer:

Outliers

Question 5.

Q_{2} = D_{5} = P_{60}

Answer:

Median

Question 6.

Partition value used in the measurement of test scores, health indicators, etc.

Answer:

Percentiles

Question 7.

Partition value is used to assess the performance of portfolio investment.

Answer:

Declies

1C. Arrange in proper order:

Question 1.

Steps to find Q_{1} and Q_{3} for continuous frequency distribution.

(a) Determine the quartile class

(b) Arrange the data in ascending or descending order.

(c) Find out cumulative frequency (cf)

(d) Write respective frequencies of the class

Options:

(1) a, b, c, d

(2) b, d, c, a

(3) b, c, d, a

(4) c, d, b, a

Answer:

(1) b, d, c, a

1D. Find the odd word out:

Question 1.

Percentile, Mercantile, Decile, Quartile

Answer:

Mercantile

Question 2.

Mean, Mode, Meridian, Median

Answer:

Meridian

Question 3.

P.C.Mahalanobis, Statistics Day, Fractile Graphical Analysis, Demand Analysis.

Answer:

Demand Analysis

Question 4.

Percentile, Health indicator, Quartile, Household income.

Answer:

Quartile

1F. Complete the following statement.

Question 1.

There are __________ deciles.

Answer:

nine

Question 2.

There are __________ percentiles.

Answer:

ninety-nine

Question 3.

There are __________ quartiles.

Answer:

three

Question 4.

50th percentile is equal to __________ deciles.

Answer:

fifth

Question 5.

25th percentile is equal to __________ quartile.

Answer:

first

Question 6.

Percentiles divide the series in __________ equal parts.

Answer:

hundred

Question 7.

Value that divides the data into 10 equal parts is called __________

Answer:

deciles

Question 8.

50th percentile is equal to __________

Answer:

5th decile

Question 9.

The value of the first quartile is __________

Answer:

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

Question 10.

The value of the 3rd quartile is __________

Answer:

\(3\left(\frac{n+1}{4}\right)^{\text {th } \text { Observation }}\)

Question 11.

Value that divides the whole set of observation into four equal parts is called __________

Answer:

Quartile

Question 12.

29th June is celebrated as __________

Answer:

Statistics Day

Question 13.

Value which divide the data into required number of equal parts are called __________

Answer:

partition values

Question 14.

Fractile graphical analysis, a statistical method was devised by __________

Answer:

Prof. P. C. Mahalanobis.

2. Distinguish between:

Question 1.

Quartiles and Deciles.

Answer:

Quartiles | Deciles |

(i) Quartiles are the values that divide the series into four equal parts. | (i) Deciles are the values that divide the series into ten equal parts. |

(ii) These are the 3 values that divide the distribution into 4 parts, each representing one-quarter of the score. | (ii) These are the 9 values that divide the distribution into 10 parts. |

(iii) It is denoted by: Q_{1}, Q_{2}, and Q_{3} |
(iii) It is denoted by D_{1}, D_{2}, D_{3}, …………. D_{9} |

(iv) 2nd Quartile is the median. | (iv) 5th Decile is the median. |

Question 2.

Deciles and Percentiles.

Answer:

Deciles | Percentiles |

(i) Deciles are the values that divide the series into 10 equal parts. | (i) Percentiles are the values that divide the series into 100 equal parts. |

(ii) These are the 9 values that divide the distribution into 10 parts. | (ii) These are the 99 values that divide the distribution into 100 parts. |

(iii) It is denoted by D_{1}, D_{2}, D_{3}, ……. D_{9} |
(iii) It is denoted by P_{1}, P_{2}, P_{3}, ……… P_{99} |

(iv) 5th Decile is median. | (iv) 50th percentile is median. |

3. Solve the following:

Type – I: Problems Based on Quartiles

Question 1.

Find Q_{1}, Q_{2} and Q_{3} from the following data:

65, 82, 68, 67, 84, 83, 66, 69, 81, 70, 85

Answer:

Q_{1} = 67, Q_{2} = 70, Q_{3} = 83

Question 2.

Find Q_{1} and Q_{3} from the following data:

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15

Answer:

Q_{1} = 6, Q_{3} = 12

Question 3.

Find first and third Quartiles from the following data:

Answer:

Q_{1} = 34, Q_{3} = 40

Question 4.

Find Q_{1}, Q_{2}, and Q_{3}?

Answer:

Q_{1} = 450, Q_{2} = 550, Q_{3} = 650

Question 5.

Find Q_{1} and Q_{3} from the following data:

Answer:

Q_{1} = 250, Q_{3} = 450

Question 6.

Find Q_{4} and Q_{3} from the following data:

Answer:

Q_{4} = 20.33 , Q_{3} = 35.25

Question 7.

Find Q_{1}, Q_{2}, and Q_{3}:

Answer:

Q_{1} = 17.22, Q_{2} = 27.41, Q_{3} = 39

Type – II: Problems Based on Decile

Question 1.

Find D_{4} and D_{8} from the following data:

20, 26, 24, 32, 22, 28, 30, 36, 34

Answer:

D_{4} = 26, D_{8} = 34

Question 2.

Find D_{1}, D_{4}, and D_{8} for the following data:

61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79.

Answer:

D_{1} = 62, D_{4} = 68, D_{8} = 76

Question 3.

Find D_{2} and D_{4} from the following data:

Answer:

D_{2} = 20, D_{4} = 40

Question 4.

Find D_{5} and D_{9}:

Answer:

D_{5} = 4, D_{9} = 5

Question 5.

Find D_{5} for the following distribution.

Answer:

D_{5} = 40.33

Question 6.

Find D_{4} and D_{6} from the following data:

Answer:

D_{4} = 30, D_{6} = 43

Type – III: Problems Based on Percentiles

Question 1.

Find Percentiles:

Calculate 50th Percentile from the following data:

20, 25, 30, 35, 40, 45, 50, 55, 60

Answer:

P_{50} = 40

Question 2.

Calculate P_{21} and P_{97} for:

Answer:

P_{21} = 3, P_{97} = 8

Question 3.

Find P_{90} from the following data:

Answer:

P_{90} = 40

Question 4.

Calculate P_{60} and P_{80} from the following data:

Answer:

P_{60} = 40, P_{80} = 48.33

Type – IV: Comprehensive Problems

Question 1.

Find Q_{1}, D_{5} and P_{45} for the following data:

Answer:

Q_{1} = 1862.64, D_{5} = 2666.67, P_{45} = 2500

4. State with reasons whether you agree or disagree with the following statements

Question 1.

Q_{2} divides the series into equal parts.

Answer:

Yes, I agree with the statement.

- Quartiles are the values of data that divide the series or data into four equal parts.
- Each represents one-quarter of the data when arranged in ascending and descending order.
- These 3 values are called Q
_{1}, Q_{2}, and Q_{3}. - Q
_{2}is nothing but the median or the middlemost value. - Hence, Q
_{2}divides the series into two equal parts.

Question 2.

The 25th percentile is equal to the first quartile.

Answer:

Yes, I agree with the statement.

- Percentile is the value that divides the series into 100 equal parts, while quartile divides the series into 4 equal parts.
- Therefore, the first quartile is equal to the 25th percentile.

Question 3.

There is no difference between quartiles, deciles, and percentiles.

Answer:

No, I do not agree with the statement.

- Quartiles are the values that divide the series into 4 equal parts, whereas deciles are the values that divide the series into 10 equal parts, while percentiles divide the series into 100 equal parts.
- Quartiles consist of 3 values, while deciles are of 9 values and percentiles are of 99 values.
- Hence, though quartiles, deciles, and percentiles are interrelated, they differ from each other.