I would only need help with e and f Using the midpoints of the indicated ranges of X;(i.e, 1.90 gram for the first class), toXifi1.85-1.95 (1.90)1.95-2.05 (2.0)2.05-2.15 (2.1)2.15-2.25 (2.2)2.25-2.35 (2.3)2.35-2.45 (2.4)2.45-2.55 (2.5)2.55-2.65 (2.6)2.65-2.75 (2.7)21231041(b) Calculate the mean leaf weight.(c) Calculate the median leaf weight using Twodifferent equations discussed in class.(d) Determine the mode of the frequencydistribution.(e) Calculate the sum of squares using twoformulas.(f) Calculate the variance, the standard deviation,and the coefficient of variation.

e) The two formulas for sum of squares is given below: SS=∑fx-μ2orSS=∑fx2-∑fx2N The value of x¯ is…

Answered: (e) Calculate the sum of squares using…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

I would only need help with e and f

Using the midpoints of the indicated ranges of X;
(i.e, 1.90 gram for the first class), to
Xi
fi
1.85-1.95 (1.90)
1.95-2.05 (2.0)
2.05-2.15 (2.1)
2.15-2.25 (2.2)
2.25-2.35 (2.3)
2.35-2.45 (2.4)
2.45-2.55 (2.5)
2.55-2.65 (2.6)
2.65-2.75 (2.7)
2
1
2
3
10
4
1
(b) Calculate the mean leaf weight.
(c) Calculate the median leaf weight using Two
different equations discussed in class.
(d) Determine the mode of the frequency
distribution.
(e) Calculate the sum of squares using two
formulas.
(f) Calculate the variance, the standard deviation,
and the coefficient of variation.

Expert Solution

Step 1

The two formulas for sum of squares is given below:

$S S = \sum f {(x - μ)}^{2} o r S S = \sum f x^{2} - (\frac{{(\sum f x)}^{2}}{N})$

The value of $\bar{x}$ is obtained as given below:

Here, m is the midpoint.

$μ = \frac{\sum_{}^{} f m}{\sum_{}^{} f} = \frac{72.6}{31} = 2.34$

The table provided above helps to find the sum of squares:

m	f	mf	$f (m - \bar{x})^{2}$	$f m^{2}$
1.9	2	3.8	0.3872	7.22
2	1	2	0.1156	4
2.1	2	4.2	0.1152	8.82
2.2	3	6.6	0.0588	14.52
2.3	5	11.5	0.008	26.45
2.4	10	24	0.036	57.6
2.5	4	10	0.1024	25
2.6	3	7.8	0.2028	20.28
2.7	1	2.7	0.1296	7.29
	31	72.6	1.1556	171.18

Formula 1:

$\begin{array}{rcl} S S & = & \sum f {(m - μ)}^{2} \\ = & 0.3872 + 0.1156 + 0.1152 + . . . + 0.1296 \\ = & 1.1556 \end{array}$

Formula 2:

$\begin{array}{rcl} S S & = & \sum f m^{2} - (\frac{{(\sum f m)}^{2}}{N}) \\ = & 171.18 - (\frac{72 . 6^{2}}{31}) \\ = & 171.18 - 170.025 \\ = & 1.155 \end{array}$

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