The sample means and variances of the observed data are needed to find the values in the sum of squares column. The given data are below. Treatment 1 Treatment 2 Treatment 3 Treatment 4 9 5 2 5 6 9 6 1 3 0 1 5 14 4 0 6 1 8 4 5 2 9 0 1 0 5 4 0 9 2 3 0 12 6 3 4 0 9 6 2 2 9 6 1 5 7 7 2 7 14 8 3 3 8 3 3 15 0 0 6 5 5 5 3 4 11 12 7 5 10 9 5 2 10 The sample mean number of pretzels consumed for Treatment 1, rounded to four decimal places, is calculated as follows. x1 = 9 + 6 + 3 + + 11 18 = 6.1111 Find the sample means of the number of pretzels consumed for the remaining treatments, rounding your results to four decimal places. x2 = x3 = x4 = The overall sample mean is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal places. = 9 + 6 + + 5 + 9 + + 2 + 6 + + 5 + 1 + + 3 74 = 5.0405 The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places. s12 = x − x 2 n − 1 = (9 − 6.1111)2 + (6 − 6.1111)2 + + (11 − 6.1111)2 17 = 21.9869 Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places. s22 = s32 = s42 =

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 20PFA

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Question

The sample means and variances of the observed data are needed to find the values in the sum of squares column. The given data are below.

Treatment 1	Treatment 2	Treatment 3	Treatment 4
9	5	2	5
6	9	6	1
3	0	1	5
14	4	0	6
1	8	4	5
2	9	0	1
0	5	4	0
9	2	3	0
12	6	3	4
0	9	6	2
2	9	6	1
5	7	7	2
7	14	8	3
3	8	3	3
15	0	0
6	5	5
5	3	4
11	12
	7
	5
	10
	9
	5
	2
	10

The sample mean number of pretzels consumed for Treatment 1, rounded to four decimal places, is calculated as follows.

x₁

9 + 6 + 3 + + 11

6.1111

Find the sample means of the number of pretzels consumed for the remaining treatments, rounding your results to four decimal places.

x₂	=

x₃	=

x₄	=

The overall sample mean

is the mean of all 74 observations and it will be used in the calculations for the variance. It is calculated below, rounded to four decimal places.

9 + 6 + + 5 + 9 + + 2 + 6 + + 5 + 1 + + 3

5.0405

The sample variance of the number of pretzels consumed for Treatment 1 is calculated as follows, with the final result rounded to four decimal places.

s₁²

x − x

	2

n − 1

(9 − 6.1111)² + (6 − 6.1111)² + + (11 − 6.1111)²

21.9869

Find the remaining sample variances of the number of pretzels consumed for each treatment, rounding the results to four decimal places.

s₂²	=

s₃²	=

s₄²	=

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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