# Modelling The Mass Of Banana Fruit By Geometrical Attributes

1595 words - 6 pages

Some selected physical characteristics of the banana such as mass, true volume, bulk density, true density, geometric mean diameter, surface area etc and their statistics such as mean, standard deviation (SD) and standard error (SE) were presented in Tab. 1. These two statistics measure the consistency of the data.
Table 1 Physical properties of banana var. Grand Nain
S.No Physical properties Mean SD Min Max SE CV,%
1 Mass (M), g 139.65 7.66 126.05 154.29 1.47 5.48
2 True volume (V), cm3 136.33 9.86 118.00 157.00 1.90 7.24
3 Ellipsoidal volume (Vell) , cm3 117.92 9.09 98.15 131.33 1.75 7.70
4 Ellipsoidal ratio 1.08 0.02 1.05 1.12 0.00 2.14
5 Fruit density (TD), g/cm3 1.03 0.03 0.98 1.11 0.01 3.20
6 Bulk density (BD), g/cm3 0.41 0.03 0.35 0.46 0.01 6.54
7 Length (L), cm 16.99 0.71 15.45 18.20 0.14 4.20
8 Width (W), cm 3.78 0.08 3.61 3.91 0.02 2.21
9 Thickness (T), cm 3.50 0.10 3.31 3.68 0.02 2.81
10 Mean diameter, cm 3.56 0.18 3.25 4.04 0.03 5.07
11 Geometrical mean diameter (Dg), cm 6.08 0.16 5.72 6.31 0.03 2.63
12 Arithmetic mean diameter (Da), cm 8.09 0.28 7.48 8.54 0.05 3.40
13 Surface area by graph (Sg) , cm2 115.84 9.31 99.17 133.28 1.79 8.04
14 Surface area by Jean & Ball, cm2 108.77 6.06 95.25 118.16 1.17 5.58
15 Surface area by McCabe, cm2 116.20 6.04 102.88 124.93 1.16 5.20
SD-Standard Deviation, Min-Minimum, Max-Maximum, SE-Standard Error, CV-Coefficient of variance

Standard deviation measures the degree to which the value of the individual sample differ from the sample mean. More number of replication decreases the standard deviation value. From the table 1, it is observed that standard deviation is ranging from 0.02 to 9.86 and found that the data are consistence within the replicates. Standard error estimated that how extent the sample mean is deviating from the population mean. Standard error value approaches zero indicates that the sufficiency of the number samples. Increase in sample size decreases the standard error value. Standard error are ranging from 0.00 to 1.90 shown in table 1 and it is observed that that all the standard error values are closely approaches to zero. Though the standard deviation values are varied in high extent, the standard error values confirm the data consistency.

Eleven regression models of three categories and their constant and coefficients are presented in Tab. 2
Table 2 Mass models of banana var. Grand Nain
S.No Models K1 K2 K3 k R2
1 M=K1L+K 8.79 - - -9.77 0.67
2 M=K1W+K 66.59 - - -111.95 0.53
3 M=K1T+K 57.44 - - -61.63 0.50
4 M=K1L+ K2 W +K 6.55 40 - -122.88 0.82
5 M=K1L+ K2 T 6.22 29.44 - -69.27 0.76
6 M=K1L+ K2 W +K3T+K 5.83 32.83 12.88 -128.62 0.83
7 M=K1Dg +K 43.24 - - -123.29 0.82
8 M=K1Sg +K 0.78 - - 48.92 0.91
9 M=K1V+K 0.72 - - 42.09 0.85
10 M=K1Vell+K 0.77 - - 49.37 0.83
K1, K2, K3- Coefficient of independent variables, K- constant, R2-coeffeicent of determination
From 1- 6 equation of first category models, it is found that the correlation coefficient (R2) of model...

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