Central tendency may be defined as the tendency of a given set of observations to cluster around a single central or middle value and the single value that represents the given set of observations is described as a measure of central tendency or location or average.
Following are the different measures of central tendency:
Results
#1. The presence of extreme observations does not affect
#2. The most commonly used measure of central tendency is
#3. Quartiles are the values dividing a given set of observations into
#4. What is the median for the following observations? 5,8,6,9,11,4
median for the following observations? 5,8,6,9,11,4
4,5,6,8,9,11
Median N＋1/2
6＋1/2= 3.5th term
3rd term＋4th term/2
6＋8/2
14/2
7
#5. The harmonic mean for the numbers 2,3,5 is
2,3,5
By using harmonic mean
H=n/∑(1/x¡)
Hormonic mean =3/(1/2 1/3 1/5)
=3/(31/30)=90/31
#6. Find the Geometric Mean of 3,6 and 12.
Geometric Mean of 3,6 and 12.
G=³√x1*x2*x3*……………Xn
G=(3*6*12)¹/³
=6
#7. The third decile for the numbers 15,10,20,25,18,11,9,12 is
15,10,20,25,18,11,9,12
Arranging the data in ascending order
9 , 10 , 11 , 12 , 15 , 18 , 20 , 25
Dί=(N＋1)*i/10
i=3
d3=(8 ＋ 1)*3/10
=9*3/10
=2.7
2nd term {3rd term-2nd term}*0.7
D 3 = 10 { 11 – 10 } × 0.7
= 10 0.7
= 10. 7
#8. What is the value of mean and median for the above data:
by using formula
Mean =∑fixi/N
median=li {N/2-Ni/Nu-NL}*c
#9. What is the HM of 1,1/2,1/3,............1/n?
Hint: 1/n(1 2 3 … n)=n＋1/2
#10. Which is the following statements is wrong?
#11. __________ is the most stable of all the measures of central tendency.
#12. Mean is of ______of types.
#13. G.M of 8,4,2 is
#14. Mode of the observations 2,5,8,4,3,4,4,5,2,4,4 is
Mode also leaves scope for more than one mode.Mode defined as the value the occurs maximum number of times.
#15. For the observations 5,3,6,3,5,10,7,2 there are _____ modes.
#16. For the values of variable 5,2,8,3,7,4 the median is
#17. _______ quartile is known as upper quartile
#18. There are ___________ percentiles.
#19. Mean for data 6,4,1,6,5,10,3 is
#20. The A.M of 1,3,5,6,x,10 is 6. The value of X is
1,3,5,6 x 10/6=6
mean=∑xi/n
25＋x=6×6
25＋x =36
x=36-25
x=11