11th class statistics important definitons for chapter 3 and short questions||measure of location|| 1st year class statistics

 Here you can see the important definitions of chapter3 that is Measure of Location

Title: 11th class statistics important definitons  for chapter 3 and short questions|| 1st year class statistics  

 

chapter 3 :Measure of Location

 (IMPORTANT   SHORT QUESTIONS) CHAPTER # 3

 

Definitions	Answers
1)      Define Mean.	It is obtained by dividing sum of values by their number. It is denoted by A.M OR .
2)      Define Median.	It is a value that divides   an arranged data into two equal parts. It is denoted by Med or .
3)      What are the merits of  Mode?	1) It is easy to understand and compute. 2) It is not affected by extreme values. 3) Mode can be determined in distributions with open end classes. 4) Mode can be located on the graph also. 5) If all the data are not given then mode can also be calculated.
4)      What is the formula of Arithmetic Mean in Group Data?
5)      Give merits of Median.	·         It is very easy to calculate and is readily understood. ·         Median is not affected by the extreme values.
6)      Give Empirical relation between Mean, Median and Mode.	Empirical relation is of two types: i-Symmetrical In which Mean=Med=Mode ii-Skewed There are two types of skewed distribution (a) Positively skewed. Mean>Med>Mode (b)Negatively Skewed Mean<Med<Mode For moderately skewed distribution the following formula holds Mode =3Med-2Mean
7)      Describe the qualities of a good average.	(i) It should be rigidly defined.  (ii) It should be based on all the observations of the series. (iii) It should be capable of further algebraic treatment. (v) It should not be affected by fluctuations of sampling.
8)      Find out arithmetic mean.  Given åx = 308 and n=7
9)      Compute the median for the following Data: 3,11,7,4,10 and   12.	Arranged data: 3, 4, 7,10 ,11,12
10)   Explain the concept of “Weighted Arithmetic Mean”	When all the values are not equally important then we assign them certain numerical values which are technically called weights. Weighted mean denoted by can be defined as Where              W= weight
11)   Define Median.	The value that divides an arranged data into two equal parts is called median.
12)   Find A.M given that D = x –45, ∑D = 25, and n = 50	As D=x-45 A=45
13)   For a certain frequency distribution, the value of Mean is 15 and Median is 20. What will be the value of Mode?	As Mode =3Med-2Mean Mode =3(20)-2(15) Mode =60-30 Mode =30
14)   Define measures of central tendency.	Measure of Central tendency is defined as “the statistical measure that identifies a single value as representative of an entire distribution .e.g. mean, median, mode, etc. OR A measure of central tendency is a measure that tells us where the middle of a bunch of data lies. The three most common measures of central tendency are the mean, the median, and the mode.
15)   Give some merits of arithmetic mean.	·         It is rigidly defined. ·         It is easy to calculate and simple to follow. ·         It is based on all the observations. ·         It is determined for almost every kind of data. ·         It is finite and not indefinite. ·         It is readily put to algebraic treatment. ·         It is least affected by fluctuations of sampling.
16)   What is the formula of median in group data?
17)   Fm = 20     F1=15     F2 =17     L=19.5   h=5, find mode.
18)   Define mode giving example.	The most repeated or the most common or the most frequent value of the data is called mode. It is denoted by . e.g  for  Data:2,7,5,87,9,3,2,9 mode =2
19)   Enlist the desirable qualities of a good average.	(i) It should be rigidly defined.  (ii) It should be based on all the observations of the series. (iii) It should be capable of further algebraic treatment. ·         (v) It should not be affected by fluctuations of sampling.
20)   In a moderately skewed distribution median is 70 and Mean is 76. find the value of mode	As Mode =3Med-2Mean Mode =3(70)-2(76) Mode =210-152 Mode =58
21)   For a certain distribution if ∑ (x – 15) = 12, ∑ (x – 18) = 0 and ∑ (x – 21) = 10 What is the value of mean and why?	By the property of mean          ..............1 And    ∑ (x – 18) = 0            ..............2 By comparing 1 and  2 we get =18
22)   If for 50 observation ∑(x – 23) = -17, then find the value of mean.	Given     ∑(x – 23) = -17 or∑D = -17 A =23
23)   Write the names of any two types of ‘Average’.	(i) Mean (ii) mode
24)   Find Median of the values : 10, 16, 12,17,13,14,11,15,18	Arranged Data: 10,11,12,13,14,15,16,17,18
25)   Write the names of any two methods for calculating Arithmetic Mean.	(i)Direct Method (ii)Coddling Method
26)   Write any two demerits of Mode.	(i)Mode is ill-defined in case of bi-modal, multi-modal series. (ii) It is not capable of further algebraic treatment. (iii) Mode is affected to a great extent by the fluctuations of sampling.
27)   Define positive skewed distribution.	The distribution is positively skewed if the right tail of a Frequency Polygon curve of a distribution is longer than left tail. OR The distribution is  positively skewed if Mean >Med>Mode
28)   Give two properties of “Arithmetic Mean”	i.         The sum of deviations of values from mean is always zero i.e.   ii.       The sum of square deviations of values from mean is always minimum i.e.           Where “A” is any constant other than mean.
29)   Find A.M given that x = 10 + 5u, ∑fu = 46 and n = 125
30)   Find Mode for the following data 2,4,5,6,4,7,6 and 10	Mode =4,6
31)   x  and y are linearly related by the equation  Find , if  = 3
32)Explain relationship among Mean Median and Mode, When distribution is symmetrical.	when distribution is symmetrical then following relationship hold among Mean Median and Mode Mean = Med =Mode
33) Give demerits of arithmetic mean.	·         The arithmetic mean is highly affected by extreme values. ·         It cannot average the ratios and percentages properly. ·         It is not an appropriate average for highly skewed distributions. ·         It cannot be computed accurately if any item is missing. ·         The mean sometimes does not coincide with any of the observed value.
34) Write any two demerits of median.	·         It is not rigidly defined. ·         To find a mode array is necessary but it is very difficult to arrange a large data.
35) A variable ‘Y’  is determined from the variable ‘X’ by the equation  Y=10-4X.Find y when X=-1,-2,0,1,2	X -1 -2 0 1 2 Y 14 18 10 6 2
36)if x1=2,x2=8, show that A.M>G.M>.H.M
37) Why is difficult to calculate geometric mean for these values (i) 0,4,8      (ii)  3,5.-2	(i) We know that if any value equals to zero then G.M is not possible. (ii) We know that if any value is negative then G.M is not possible.
38) Define geometric mean.	The nth positive root of the product of n positive values is called geometric mean. It is denoted by G.M.  Symbolically    for ungroup data
39) Given that and n=5. Find mean.	Since
40) Give various methods of computing arithmetic mean for group data.
41) Define deciles.	Deciles The values that divide an arrayed data into ten equal parts are called quartiles. They are denoted by D1, D2, and D3 ...D9. Symbolically For ungroup Data  Where    m = 1,2,3,4... 9 For group Data Where      Lower class boundary of Dm   group                    h = class width of Dmgroup                  f = frequency of Dmgroup                  c = cumulative frequency of the class preceding the Dmgroup Where m = 1,2,3,4... 9

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