Test: Relation between Central Tendencies - Class 10 MCQ

Median = L + [ (N/2 – F) / f ]C
=30+[(50-33)/30]*10
=35.66
Mode=L+
=30+ 
=35.45
Mean=(3Median-Mode)/2
 =(106.98-35.45)/2=35.76

A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other. The mean, the median, and the mode are each equal for these type of data. In a perfectly symmetrical distribution, the mean and the median are the same. In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median.

To find Mode
Mode=L+ 
Where L=lower limit of the modal class  = 40
f1 = modal class frequency.= 65
f2 = just after the modal class frequency.=46 
f0 = just previous the modal class frequency=34
C = Class size=10
Mode = 
=46.2
Mode = 3 Median – 2 Mean
46.2 =3*46-2Mean
2Mean=138-46.2=91.8
Mean=91.8/2=45.9

We have
Mode=L+ 
Where L=lower limit of the modal class =160
f1= modal class frequency.=28
f2 = just after the modal class frequency.=24
f0 = just previous the modal class frequency=17
C = Class size=10
Mode= 
=167.3
Mode = 3 Median – 2 Mean
Mean=(3*166.79-167.3)/2=168.03

A measure of central tendency is a measure that represents the center point or typical value of a data. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution.It can also be viewed as the tendency of data to cluster around a middle value.Standard deviation as the name suggests is a measure of the deviation. Deviation means change or distance. But change is always followed by the word 'from'. Hence standard deviation is a measure of change or the distance from a measure of central tendency  which is normally the mean. Hence, standard deviation is different from a measure of central tendency.