How To Find Arithmetic Mean Video Lecture - Class 10

good morning children today we shall
learn about the measures of central
tendency of data starting with
arithmetic mean as we saw in the story
Keshav was a fisherman he didn't earn
the same every day if he was asked about
his income what should he say here is
his income for a week and as we see all
are different
Monday he earned rupees two hundred and
thirty five Tuesday he earned five
hundred and fifty rupees witness day it
was six hundred and seventy five
Thursday it was seven hundred Friday
six hundred and fifty and Saturday 385
he cannot give the details of his
earnings for the whole week to answer
the question there has to be a single
value which represents his earning for
the whole week such single values which
represent the central value or the
average value of data or in other words
are typical of the distribution of data
are called measures of central tendency
of that data so the measure of central
tendency refers to a single value which
represents the whole data the types of
data can be different so there are
different measures of central tendency
for different kind of data you know
there are three types of measures of
central tendency for different kind of
data the arithmetic mean median and the
mode so today we shall learn when and
how to represent data using arithmetic
mean in real life we find many instances
of arithmetic mean
for example the average test petting
score of famous Indian cricketer Sachin
Tendulkar is almost 54 here 54 is a
measure of central tendency which
represents his test score data
or the average score of the boy who
stood first in the class was 85 in all
the subjects here by average we mean the
arithmetic mean
why do we need arithmetic mean Khushi
got different scores in different
subjects she scored 80 70 74 93 77 and
86 in six different subjects
she needs 75 average or mean score to
get admission in a good school
why arithmetic mean because arithmetic
mean gives general idea about her score
that is it gives the idea about what
kind of score she gets so the total
marks scored in all the six subjects is
equal to 480 marks how to find the
average or the arithmetic mean here
first we add all the marks which are 80
plus seventy plus 74 plus 93 plus 77
plus 86 and we get 480 marks then we
divide the total by the number of
subjects which we know is equal to six
so we get 480 divided by six which is
equal to 80 so the mean is equal to 80
thus we divide the sum of all the values
by the number of values to get the mean
or the average high mean score gives
general idea that she scores good marks
in each subject
take another example in cricket a
batsman doesn't scored the same run all
the matches true in some matches he
plays good some matches he wouldn't be
able to do that well for example a
batsman scored 3547 1295 63 and 70 in
six matches so the total runs made is
equal to 322 and six matches the number
of matches played is equal to six if we
divide the total which is 322 by the
number of matches which is six we get
fifty three point six six as the average
or the mean fifty three point six six
represents his padding score data it
gives general idea about his performance
it means he may play bad in some matches
but his overall performance is good
which assured by the average of the mean
here which is fifty three point six six
in the story
Katia's average or the mean earnings
increased after using the mobile phone
in his business say some week he earned
rupees 235 550 675 700 650 and 385 in
the six days of a week here we see the
earnings are different so the total
earnings made in a week is equal to
three thousand one hundred and ninety
five if we divided by seven we get the
mean which is rupees four hundred and
fifty six point four
- thus his daily average or mean income
was rupees 456 0.42 someday he earned
less someday he earned more but the
overall income was could thus mean gives
the general idea about the values in the
data now you may wonder does the
arithmetic mean always represent the
central tendency of data correctly let
us take some examples and figure this
out
you know if the data has extreme values
which are much larger or smaller than
the other values then the mean doesn't
give proper idea about the data for
example Manilal sweetshop is not doing
well in a week he sells the sweets as
follows Monday 50 Tuesday 75 Witness day
85 Thursday 55 Friday 750 Saturday 90
and Sunday hundred so we see on Friday
lots of sweets were sold because it was
a festival day so total weekly income
rose to rupees 1,234
200 and 5/7 then what do we get we get
the mean as 172 but as we see his shop
is not doing well and he rarely makes
rupees 172 per day so this arithmetic
mean of rupees 172 is not giving proper
idea about his earnings it is because
rupees 750 is an extreme value which
made create a difference in the sum and
thus made greater difference in the mean
so now we know the arithmetic mean gives
general idea about the data in many
instances in real life like we decide
whether a person earns good or not from
his daily or monthly mean income we know
how a good batsman is from his mean
score a student is also judged by his
mean score
so remember children the single values
which represent the central value or the
average value of whole data are referred
to as measures of central tendency of
that data one such measures is the
arithmetic mean and what is arithmetic
mean the arithmetic mean of a given data
is defined as the sum of the values of
the data divided by the total number of
values so the mean is equal to sum of
all values divided by the total number
of values that's all for now bye bye
children