Table of contents

1. Introduction to Genetics51m
2. Mendel's Laws of Inheritance3h 37m
3. Extensions to Mendelian Inheritance2h 41m
4. Genetic Mapping and Linkage2h 28m
5. Genetics of Bacteria and Viruses1h 21m
6. Chromosomal Variation1h 48m
7. DNA and Chromosome Structure56m
8. DNA Replication1h 10m
9. Mitosis and Meiosis1h 34m
10. Transcription1h 0m
11. Translation58m
12. Gene Regulation in Prokaryotes1h 19m
13. Gene Regulation in Eukaryotes44m
14. Genetic Control of Development44m
15. Genomes and Genomics1h 50m
16. Transposable Elements47m
17. Mutation, Repair, and Recombination1h 6m
18. Molecular Genetic Tools19m
- Genetic Cloning
  9m
- Methods for Analyzing DNA
  9m
19. Cancer Genetics29m
- Overview of Cancer
  21m
- Cancer Mutations
  7m
20. Quantitative Genetics1h 26m
21. Population Genetics50m
- Hardy Weinberg
  19m
- Allelic Frequency Changes
  31m
22. Evolutionary Genetics29m

20. Quantitative Genetics

Analyzing Trait Variance

Genetics

20. Quantitative Genetics

Analyzing Trait Variance

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1:15 minutes

Problem 31b

Textbook Question

A total of 20 men and 20 women volunteer to participate in a statistics project. The height and weight of each subject are given in the table. Calculate the mean, variance, and standard deviation for height and weight in men and women.

Verified step by step guidance

Organize the data by separating the height and weight values for men and women into four distinct groups: men's heights, men's weights, women's heights, and women's weights.

Calculate the mean (average) for each group using the formula:

mean = \frac{\sum x}{n}

, where

x

represents each individual measurement and

n

is the number of individuals (20 in this case).

Compute the variance for each group by first finding the squared difference between each measurement and the mean, then averaging these squared differences using the formula:

variance = \frac{\sum {x - mean}^{2}}{n}

Determine the standard deviation for each group by taking the square root of the variance, expressed as:

standard deviation = √ variance

Summarize the results by listing the mean, variance, and standard deviation for height and weight separately for men and women, ensuring clarity in the presentation of each statistical measure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mean

The mean is the average value of a data set, calculated by summing all observations and dividing by the number of observations. It provides a measure of central tendency, representing the typical value in the data, such as average height or weight.

Variance

Variance measures the spread or dispersion of data points around the mean. It is calculated as the average of the squared differences between each data point and the mean, indicating how much the values vary within the group.

Standard Deviation

Standard deviation is the square root of the variance and expresses data variability in the same units as the original measurements. It quantifies the typical distance of data points from the mean, helping to understand the consistency of height or weight within men or women.

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Related Practice

Textbook Question

Suppose the mature height of a plant is a multifactorial trait under the control of five independently assorting genes, designated A, B, C, D, and E, and five environmental factors. There are two alleles of each gene (A₁, A₂, etc.). Each allele with a subscript 1 (i.e., A₁) contributes 5 cm to potential plant height, and each allele with a 2 subscript (i.e., A₂, etc.) contributes 10 cm to potential plant height. In other words, a genotype containing only 1 alleles (A₁A₁B₁B₁C₁C₁D₁D₁E₁E₁) would have a potential height of [(10)(5)]=50cm, and a genotype with only 2 alleles (A₂A₂B₂B₂C₂C₂D₂D₂E₂E₂) would have a potential height of [(10)(10)]=100cm.The five environmental factors are (1) amount of water, (2) amount of sunlight, (3) soil drainage, (4) nutrient content of soil, and (5) temperature. Each environmental factor can vary from optimal to poor. If all factors are optimal, assume that full potential height is attained. However, if one or more of the environmental factors is less than optimal, then height is reduced. The state of each environmental factor has an effect on growth. In this exercise, we'll assume that the growth is affected according to the following scale:Environmental Factor State Height LostOptimal (O) 0 cmGood (G) 4 cmFair (F) 8 cmMarginal (M) 12 cmPoor (P) 16 cmThus, for example, if one environmental factor is optimal, two are good, one is fair, and one is marginal, the loss of potential height is . If the loss of height potential is greater than the height potential of the plant, the plant does not survive.How many 1 and 2 alleles must be present to give a height potential of 80 cm?

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views

Textbook Question

Suppose the mature height of a plant is a multifactorial trait under the control of five independently assorting genes, designated A, B, C, D, and E, and five environmental factors. There are two alleles of each gene (A₁, A₂, etc.). Each allele with a subscript 1 (i.e., A₁) contributes 5 cm to potential plant height, and each allele with a 2 subscript (i.e., A₂, etc.) contributes 10 cm to potential plant height. In other words, a genotype containing only 1 alleles (A₁A₁B₁B₁C₁C₁D₁D₁E₁E₁) would have a potential height of [(10)(5)]=50cm, and a genotype with only 2 alleles (A₂A₂B₂B₂C₂C₂D₂D₂E₂E₂) would have a potential height of [(10)(10)]=100cm.The five environmental factors are (1) amount of water, (2) amount of sunlight, (3) soil drainage, (4) nutrient content of soil, and (5) temperature. Each environmental factor can vary from optimal to poor. If all factors are optimal, assume that full potential height is attained. However, if one or more of the environmental factors is less than optimal, then height is reduced. The state of each environmental factor has an effect on growth. In this exercise, we'll assume that the growth is affected according to the following scale:Environmental Factor State Height LostOptimal (O) 0 cmGood (G) 4 cmFair (F) 8 cmMarginal (M) 12 cmPoor (P) 16 cmThus, for example, if one environmental factor is optimal, two are good, one is fair, and one is marginal, the loss of potential height is . If the loss of height potential is greater than the height potential of the plant, the plant does not survive.List two genotypes that have a height potential of 80 cm.

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Textbook Question

A three-gene system of additive genes (A, B, and C) controls plant height. Each gene has two alleles (A and a, B and b, and C and c). There is dominance among the alleles of each gene, with alleles A, B, and C dominant over a, b, and c. Under this scheme, the dominant genotype for a gene contributes 10 cm to height potential, and the recessive genotype contributes 4 cm.What is the height potential of a plant that is homozygous for all three recessive alleles?

579

views

Textbook Question

A three-gene system of additive genes (A, B, and C) controls plant height. Each gene has two alleles (A and a, B and b, and C and c). There is dominance among the alleles of each gene, with alleles A, B, and C dominant over a, b, and c. Under this scheme, the dominant genotype for a gene contributes 10 cm to height potential, and the recessive genotype contributes 4 cm. What is the height potential of a plant that is homozygous for all three dominant alleles?

733

views

Textbook Question

A total of 20 men and 20 women volunteer to participate in a statistics project. The height and weight of each subject are given in the table. Compare the numerical values with the visual distribution of heights and weights you drew in the histograms and describe whether you think your visual impression matches the numerical values.

317

views

Textbook Question

A three-gene system of additive genes (A, B, and C) controls plant height. Each gene has two alleles (A and a, B and b, and C and c). There is dominance among the alleles of each gene, with alleles A, B, and C dominant over a, b, and c. Under this scheme, the dominant genotype for a gene contributes 10 cm to height potential, and the recessive genotype contributes 4 cm. What is the height potential of the F₁ progeny of the homozygous plants identified in (a) and (b) of this problem?

401

views

Textbook Question

A three-gene system of additive genes (A, B, and C) controls plant height. Each gene has two alleles (A and a, B and b, and C and c). There is dominance among the alleles of each gene, with alleles A, B, and C dominant over a, b, and c. Under this scheme, the dominant genotype for a gene contributes 10 cm to height potential, and the recessive genotype contributes 4 cm. What are the phenotypes and proportions of each phenotype among the F₂?

563

views

Textbook Question

A total of 20 men and 20 women volunteer to participate in a statistics project. The height and weight of each subject are given in the table. Draw one histogram for the height of the subjects and a separate histogram for weight. Use different colors for men and women so that you can visually compare the distributions by sex and plot weights in 10-lb intervals (i.e., 90–99 lb, 100–109 lb, 110–119 lb, etc.).

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