Find out Mean, Median, Mode, Standard deviation, Standard Error and Co-efficient of variance using Neem leaves

1. Find out Mean, Median, Mode, Standard deviation, Standard Error and Co-
efficient of variance using Neem leaves
Aim:
To find out Mean, Median, Mode, Standard Deviation, Standard error and Coefficient of
variance using neem leaves.
Principle:
Measures of central tendency is a summary statistic that represent the center point or typical
value of a data set. This value lies between the minimum and maximum values. It is generally
located in the center or middle of the variables. While measures of central tendency are used to
estimate "normal" values of a dataset, measures of dispersion are important for describing the
spread of the data, or its variation around a central value. Two distinct samples may have the
same mean or median, but completely different levels of variability or vice versa. In order to
have a correct analysis of a much scattered series, a study of the extent of the scatters around on
average should be studied.
Procedure:
Serrated edges of neem leaves are taken as a raw data or ungrouped data. They are
arranged in an array. Then the data are grouped with class interval.
Statistical Method:
Following statistical methods are used in the analysis of data.
Mean:
It is defined as the sum of measurements divided by the total number of measurements.
When data are grouped the mean is calculated by the formula.
𝑥̅ =
∑𝑓𝑥
𝑁
𝑥̅ = Sample Mean
∑ = Summation
f = Frequency
x = Individual measurements
N = Total number of leaves in the samples

2. Mean for grouped data with class interval is calculated by the formula.
𝑥̅ =
∑𝑓𝑚
𝑁
∑ = Sum
f = Frequency
m = Midvalues
N = Total number
Median:
Median of a sample is the middle number in a array when the number of observation is
odd.
Median is = Value of (
𝑁+1 𝑡ℎ
2
) items
Median for grouped data with class interval is calculated by the formula.
Median = 𝐿 + (
𝑁
2
−𝑐𝑓
𝑓
) × 𝑐
L = Lower limit of median class
N = Total frequency
Cf = Cumulative frequency prior to median class
C = Class interval of the median class
F = Frequency of the median class
Mode:
It is defined as the value of variable which occurs most frequency in a distribution mode
for grouped data with class interval is calculated by the formula.
Mode = 𝐿 + [
∆1
∆1+∆2
] × 𝐶
L = Lower limit of the mode class
∆1 = The difference between the frequency of modal class (f1) and the
frequency proceeding modal class (f0):∆1 = f1 – f0
∆2 = The difference between the frequency of the modal class (f1) and the
frequency of succeeding modal class (f2): ∆2 = f1 – f2.

3. C = Class interval of modal class.
F1 = Frequency of modal class
F0 = Frequency of proceeding modal class
F2 = Frequency of succeeding modal class
Standard Deviation:
It is defined as the positive square root of mean of the squares of deviation from the mean
standard deviation for a grouped data can be calculated by the formula
SD =
√∑𝑓(𝑥−𝑥̅)2
∑𝑓
SD for the data with class interval can be calculated by the formula.
SD =
√∑𝑓(𝑚−𝑥̅)2
∑𝑓
Co-efficient of variation:
The measure is obtained by dividing standard deviation by mean and multiplied by 100.
CV =
𝑆𝐷
𝑀𝑒𝑎𝑛
× 100
Standard Error:
Standard error is the ratio of standard deviation of the sample divided by square root of
the total number of deviation.
Standard error =
𝑆𝐷
√ 𝑁
Raw data:

4. Systematic data:
Result:
Mean =
Median =
Mode =
Standard deviation =
Standard error =
Co-efficient of variation =
Classes
(x)
Mid value
(m)
Frequency(f) fm 𝒅 = (𝒎 − 𝒙̅) 𝒅 𝟐
𝒇 × 𝒅 𝟐