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Q.10: State the algebraic properties of A.M Ans: n (i) Sum of deviation of values from their mean is zero i.e. (X i 1 i X) 0 (ii) Sum of squares of deviation from mean is minimum i.e. n n ( X i X )2 i 1 (X i 1 i P.M ) 2 whereP.M X . n1 X (iii) Combined mean= X c n1 (iv). A.M is affected by change of origin and scale i.e. if Y a bX then Y a bX Q.11: What is difference between weighted and un-weighted mean Ans: In un-weighted mean all the items are equally important. In weighted mean all the items are not equally important. Q.12: Define Geometric mean? Ans: Nth root of product of “n” positives value is called Geometric mean. OR The geometric mean (G.M) is defined as the nth root of the product of n positive values. If X1, X2…..Xn be n positive values, then geometric mean is defined by GM n X1 X 2 ........ X n 1 G.M ( X 1 X 2 ........... X n ) n Ungrouped data f log X G.M anti log Grouped data f Q.13: write down the advantages and disadvantages of geometric mean. Ans: Advantages of Geometric mean Disadvantages of Geometric mean 1. It is well defined 1. It is not suitable for every kind of 2. It uses all the values data 3. It is stable for more action 2. It does not exits if any value is 4. It is stable in repeated Zero experiments 3. It cannot be calculated if any value is negative Q.14: Define Harmonic mean (H.M) Ans: Ratio between number of values and sum of their reciprocals is called Harmonic mean. n H .M For ungroup data 1 X f H .M For group data f X Q.15: Down the advantages and disadvantages of Harmonic mean. Ans: Advantages of Harmonic mean Disadvantages of Harmonic mean i. It is well defined i. It gives more weight to small ii. It uses all the values values iii. It is stable for more action ii. It does not exits if any value is Zero iii. It is highly affected by extremely small values. Q.16: Describe the ratio between A.M, G.M, and H, M? A.M>G.M>H.M If all the values are not equal A.M=G.M=H.M if all the values are equal Q.17: Define Median? Ans: The value which divides the array data into two equal parts is called Median. It is central value if number of values is odd and means of two central values if number of values is even. Q.18: Write down the Advantages and Disadvantages of Median Ans: Advantages of Median Disadvantages of Median i. It is well defined i. It is not based on all values ii. Its graphic location is possible ii. It is not able for more action iii. It is not affected by extreme iii. For large number of values values arrangement of data is difficult iv. It can be calculated for open end frequency distribution Q.19: Define Mode and describe its Advantages and Disadvantages? Mode Ans: The most repeated value of data is called Mode. A data may have more than one values of mode. A data having one mode is called UNI-MODEL. Similarly data having two modes is called Bi-Modal. f m f1 X l h Group data f m f1 f m f 2 Advantages of Mode Disadvantages of Mode i. Its graphical location is possible i. It is ill defined ii. It is not affected by extreme ii. It is not based on all values values iii. It is not able for more action iii. It can be calculated for every kind iv. For small number of values it may of data not exist iv. It can be calculated for open end frequency distribution Q.20: What are the limitations of Mode? i. It is ill defined ii. It is not based on all values iii. It is not able for more action iv. For small number of values it may not exist Q.21: Define Quartiles, Deciles, and Percentiles? Ans: Quartiles: The values, which divide the array data into four equal parts, are called Quartiles. There are three Quartiles Q1, Q2 and Q3. Q1 is lower Quartiles Q2 is Median and Q3 is called Upper Quartiles. Deciles: The values which divide the array data into ten equal parts are called Deciles. There are nine Deciles, denoted D1, D2, D3………..D9. Percentiles: The values, which divide the array data into 100 equal parts, are called Percentiles. There are 99 Percentiles, denoted as P1, P2, P3…….P99. Q.22: Under what circumstances (condition) A.M, G.M, H.M, MEDIAN and MODE can be used properly to describe the measures of central tendency? Ans: A.M: Suitable when there are no very small or large values in the data. G.M: It is suitable if the data is in the form of percentages H.M: It is suitable if data is in the form rates and ratios. MEDIAN: It is suitable when middle most value is required or distribution is skewed MODE: it is suitable, when most common value is required

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