This document discusses degree of freedom in the context of a case study analyzing packet weights from three spice manufacturing plants. It defines degree of freedom as the number of independent variables that can vary in a data sample. For this case study, ABC Limited collected 35 samples each from 3 plants and found that the packet weights varied between plants. The degree of freedom for total sum of squares was 119, for sum of squares within groups was 117, and between groups was 2. The analysis showed packet weights differed between at least one plant, rejecting the null hypothesis that weights were equivalent.

1. Degree Of Freedom
Group 6 Case Study
GauravChandak - 204 Nishant A – 220
ParasWadhwa - 223 Rahul Nair - 226
Sudiksha Mehta – 238 Vipin Dhonkaria – 245
Yougal Kargaonkar–247

2. Introduction
It is defined as the maximum number of logically independent variables
which are values that have the freedom to vary, in the data sample
For ex. If in a class of 10 students, we know the average weight of all the
student and individual weight of 9 students, so we can calculate the weight
of 10th student. So in this case, degree of freedom is 10-1= 9
So, for this case, If n is total number of sample, then Degree of freedom is
given by: DF= n-1

3. Case Study Problem Statement
ABC Limited is a leading company that manufactures and packages spices
across three cities.The plants are operated in Jaipur, Lucknow and Delhi which
produces chilly powder packets of 100gm.
The company is putting a label of 100 gm on each packet and want to ensure
whether every packet from different plants contains same weight or not.
The Operation Manager of the company had collected 35 samples each from
all three plants and then try to figure out whether the packets from all the
plants are equal in weights.

4. Plant Wise Sample Packet Weights
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Sample
Packet Weights
Jaipur Lucknow Delhi

5. ANOVA Results

6. Degree Of Freedom For Sum Of Squares
▪ Degree of freedom for sum of squares
▪ Degree of Freedom for Sum of Squares within group = N-C
▪ Reason :We have average values for C columns so our degree of freedom reduces
to N-C
Degree of Freedom for Sum of Squares between group = C-1
Reason :We have average values for overall mean so our degree of freedom reduces
to C-1
Degree of Freedom forTotal Sum of Squares
= N-1
Reason :We have average values for total sum of square so our degree of freedom
reduces to N-1

7. Results And Conclusions
Value of F is greater than F critical which lies outside the confidence
interval. So we reject the null hypothesis.
Also, p value< 0.025 which does not contained in confidence interval
We can conclude that weight of packets from at least one of the plant is not
equivalent from the other two.

8. Conclusions
Degree of freedom is highly related to the sample size. As sample size
increases from 35 to 40 degree of freedom also increase
df for total sum of squares = N-1 = 120-1 = 119
df for sum of squares within groups = N-C = 120-3 = 117
p value decreases with increase in degree of freedom and there are high
chance of rejection of null hypothesis.

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