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…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 38HP

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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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