1. Project Submitted
On
“Business Statistics”
By
Rajkumar Jangid
(BBA 1st Year)
106/10 civil lines,Ajmer 305001
Website: www.dezyneecole.com
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2. ARITHMATIC MEAN
The mean is obtained by dividing the some of observed values
by the number of observation, n. Although data points fall above
or on the mean it can be considered a good estimate for producting
subsequent data points.
X = X
N
Calculation of Mean
1. Individual Series : In individual series we can find out
arithmetic mean by two methods :
a. Direct Method : In direct method we find out the
total of all values and divided by total of items.
b. Shortcut Method : It is used on account of the fact
that at it makes simple calculation.
2. Discrete Series : In discrete series also arithmetic mean
is calculated according two methods :
a. Direct Method : Under direct method arithmetic
mean is calculated in the following way :
i. Every size is multiplied with its frequency.
ii. Some of multiplied values is found out.
iii. This some is divided by total number of frequency.
b. Shortcut Method : This method involves the
following procedure :
i. Take a value as assumed mean.
ii. Find the deviations of all the values from assumed
mean.
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3. iii. Find the products by multiplying deviations with
respective frequency.
iv. Find the sum of the products.
3. Continuous Series : Arithmetic mean in continuous
series may be calculated by the following methods :
a. Direct Method : While calculating arithmetic mean
by direct method in a continuous series, we convert the
series in a discrete from by finding out the mid values
and rest of the procedure is the same as that in case of
discrete series.
b. Shortcut Method : Under this method also we
convert the series into discrete from by finding out the
mid-values.
c. Step Deviation Method : Under this method, the
deviations are divided by a common factor (values), so
as to make the figures smaller for easier calculation.
ADVANTAGES OF ARITHMETIC
MEAN
 Simplicity : Arithmetic mean is easy to understand
and calculate.
 Certainty : Arithmetic mean is always also
determine is certainty while for some other averages
there is no certainty that they will be determined.
 Based on all the values : Arithmetic is based on
all the values.
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4. DISADVANTAGES OF ARITHMETIC
MEAN
 Unreal : Sometimes, in arithmetic we find such a value
which seems to be unreal
 Cannot be Calculated by Inspection Only :
The arithmetic mean cannot be calculated by Inspection
only while some other averages can be calculated by
inspection.
 All Real Values must be known : Unless we know
all the real values we cannot calculate arithmetic mean.
MODE
The mode of a set of data is the value which occurs most
frequently. The excel syntax for the mode is MODE.
Calculation of Mode
1. Individual Series : In an individual series we cannot
calculate mode without converting it into a discrete series as
the frequency of every size is one.
2. Discrete Series : In discrete series we calculated mode
by the following methods :
a. By Inspection : Where the distribution of
frequencies is regular, mode may be calculated by a
simple inspection.
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5. b. By Grouping Method : Where the distribution of
frequencies is irregular, mode is calculated by grouping,
since by inspection the mode can’t be found out.
3. Continues Series : While calculating mode in
continuous series, we must see that the series is exclusive and
class intervals are equal.
Formula :
1
Z = l1+ *i
1 + 2
ADVANTAGES OF MODE
 Calculation Simple : Calculation of mode is simple.
Sometimes in individual and discrete series it can be found
out by inspection only.
 Graphical Representation : Mode can be calculated
graphically also.
 Use in Quantitative Facts : Mode is also used for
describing the quantitative data.
DISADVANTAGES OF MODE
 Uncertainty : Calculation is mode not always certain
 Not Based on All the Values : Mode is not based on
all the values of a series as mode is not affected by extreme
values.
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6.  Algebraic Treatment Not Possible : After
calculating mode we cannot algebraically analyse it as it is
not based on all the items.
MEDIAN
The median is the middle value of a set of data containing an
odd number of values, or the average of the two middle value of a
set of data with an even number of values. The median especially
helpful when separating data into two equal size bins. The excel
syntax to find the median is MEDIAN.
Calculation of Median
1. Individual Series : For calculating median in the
individual series, we will arrange the series in ascending or
descending order. Then write the serial numbers. After
arrange and write the serial number we will use the following
formula :
n 1
M=
2
2. Discrete Series : For calculating the median in discrete
series, we will arrange the series in ascending or descending
order. Then find out cumulative frequencies. Use this formula
to out the median.
n 1
M=
2
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7. 3. Continuous Series : In continuous series the median
will be calculated, convert the series into exclusive continuous
form. The find out cumulative frequencies. After calculating
it find median group the median group is seen in cumulative
frequency. We use this formula :
M = l1+ i (m-c)
f
ADVANTAGES OF MEDIAN
 Simple : It can be calculated as well as understood easily by
all.
 Specific : It is specific in every type of series, while other
averages may not be clear sometimes.
 Least Affected by Extreme Values : Median is
least affected by extreme values.
DISADVANTAGE OF MEDIAN
 Lack of Algebraic Treatment : Algebraic
treatment of median is not possible.
 Effect of Sampling : Median is affected much by
sampling as comparised to other averages.
 Arrangement Required : To calculate median, data
are the arrange in an ascending order or a descending order
while it is not necessary of other averages.
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8. RELATIONSHIP BETWEEN MEAN,
MODE AND MEDIAN
With the help of Numerical Question :
Ques. (a) If the value of mean ( X ) = 5 and mode (Z) = 5, find out
the value of median (M).
(b) In a moderately symmetrical distribution :
(i) Median and Mean are 24 and 25, calculate mode.
(ii) Mode and Median are 20 and 22, calculating
arithmetic mean.
(iii) Mode and mean are 30 and 33, calculate median.
Solve : (a) given: X =5, Z=5
Z= 3M – 2 X or -3M = 2 X +Z
M = 2 X +Z = 2 * 5 + 5 = 10 + 5 = 15 = 5
3 3 3 3
(b) (i) Z = 3M - 2 X or
Z = 3*24 – 2 * 25 or
Z = 72 -50 = 22
Mode is 22
(ii) Z = 3M/0 2 X or 2 X = 3M – Z
2 X = 3 *22 -20 or 66 – 20 = 46
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9. X = 46/2 = 23
Arithmetic mean = 23
(iii)Z = 3M - 2 X or -3M = 2 X + Z or
M = 2 X +Z = 2*33+30 or 66+30 or
3 3 3
96 = 32
3
Median = 32
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