I had copied and pasted my lab, I don't understand how to do the histogram and statistical portion of this lab. Item 5: In-Lab Exercises (15 points)

Exercise 1: Canine Variability

In this part of the lab, you will first collect statistical data using Table 1: Canine Length for a Sample of African Apes (Chimpanzees and Gorillas), and then you will create a series of histograms using those statistics. Follow the directions below to complete Table 2: Chart for Summary Statistics and Frequency Tabulations of Canine Length Data and the seven histograms based upon the various samples from the full data set.

Task 1: Analysis of Samples

Step 1: Summary Statistics

Identify the sample that you should be working with from the data in Table 1. Calculate the following summary statistics using a calculator. Write the results in Table 2 under the appropriate sample. The following definitions will help you:

• N is the number of all of the values in this sample.
• Minimum is the smallest value in the sample
• Maximum is the largest value in the sample
• Mean = the sum of all values in the sample divided by N (already calculated for you)
• Standard Deviation is calculated for you.
• Coefficient of Variation is:

Step 2: Frequency distribution for Sample

Use the lower part of the appropriate sample column in Table 2 to tally up the frequency of the data points in the ranges. You should make a tally mark for each occurrence of a data point within the frequency range. The last cell asks you for N again. This is a way to catch any errors by counting up your tally marks to make sure that you identified all of them. If your two N's do not match, then you have made an error somewhere.

Once you have completed that sample on Table 2, you should make a frequency histogram in the lower part of Figure 1, in the space for that sample's histogram.

Repeat Step 1 and 2 until you have completed Histograms A-G.

Table 1: Canine Length for a Sample of African Apes (Chimpanzees and Gorillas)

Spec. Number	Max Length of Canine (mm)
1	19.4
2	20.4
3	23.0
4	21.2
5	20.5
6	21.7
7	19.0
8	14.5
9	14.3
10	14.6
11	15.9
12	14.4
13	14.5
14	12.5
15	10.8
16	11.7
17	11.2
18	11.7
19	11.0
20	12.2
21	12.3
22	14.3
23	15.3
24	14.0
25	12.5
26	13.5
27	15.5

Table 2: Chart for Summary Statistics and Frequency Tabulations of Canine Length Data

Statistic	Sample A	Sample B	Sample C	Sample D	Sample E	Sample F	Sample G
Name of Sample	All data	Species 1 (1-13)	Species 2 (14-27)	Sp 1 Male (1-7)	Sp 1 Fem (8-13)	Sp 2 Fem (14-20)	Sp 2 Male (21-27)
Number (N)
Maximum
Minimum
Mean	15.26	17.95	12.75	20.74	14.7	11.59	13.91
Standard Deviation	3.64	3.49	1.60	1.37	.60	.62	1.31
Coefficient of Variation
Frequency Data
10-11.9 mm
12-13.9 mm
14-15.9 mm
16-17.9 mm
18-19.9 mm
20-21.9 mm
22-23.9 mm
24-25.9 mm
26-27.9 mm
N=

Figure 1: Histograms of Canine Length

Histogram ASample of All Data (1-27)

10
9
8
7
6
5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Histogram BSample of Species 1 (1-13)

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5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Histogram CSample of Species 2 (14-27)

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5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Histogram DSample of Species 1 Males (1-7)

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5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Histogram ESample of Species 1 Female (8-13)

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5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Histogram FSample of Species 2 Female (14-20)

6
5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Histogram GSample of Species 2 Male (21-27)

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5
4
3
2
1
	10-11.9	12-13.9	14-15.9	16-17.9	18-19.9	20-21.9	22-23.9	24-25.9	26-27.9

Part 2: Discussion Questions for Exercise 1: Canine Variability

1. If you were to only look at the total sample of canine data (Sample A All Data), would you conclude that you were looking at more than one species, or one very sexually dimorphic species? What data or statistics influence your interpretation?

1. When you subdivided the sample of All Data into two different species, what happened to the standard deviations?What happened to the coefficients of variation?

1. Why is it relevant to understand sexual selection and sexual dimorphism when interpreting canine data?

1. What factors would you have to take into account in interpreting a fossil record that consisted only of ape canines?Would you be likely to overestimate and/or underestimate the number of species represented by relying upon a feature that can be highly sexually dimorphic?

Exercise 2: Molar variability

In this section you will compare data taken from the molars of several ape species and use statistical methods to evaluate the hypothesis that the early members of Homo comprise a single species (Lump Hypothesis).

Part 1: Calculate the Coefficient of Variation

Table 3 gives some descriptive statistics for the bucco-lingual breadth of molars from three australopith species and early Homo. Here, all of the specimens of early Homo are grouped as one species (Lump Hypothesis).

Calculate the coefficient of variation (CV) for each of these species

Write your answer in Table 3 below.

Table 3: Hominoid Maxillary Bucco-lingual Breadth

Species	sex	N	mean	min	max	SD	CV
Gorilla gorilla	male	20	16.6	14.3	18.3	0.9
	female	20	15.6	14.0	17.2	0.9
	All	40	16.1	14.0	18.3	1.0
Pan troglodytes	male	13	11.7	11.0	12.8	0.5
	female	11	11.4	10.2	12.4	0.6
	All	24	11.6	10.2	12.8	0.6
A. africanus	All	15	15.3	13.8	17.2	1.0
P. robustus	All	16	16.0	14.2	17.0	0.9
early Homo	All	10	14.6	13.5	17.6	1.4

Part 2: Discussion Questions for Exercise 2: Molar Variability

1. Look at the coefficients of variation in Table 3.Which species exhibits greater variation, gorillas or chimpanzees?

1. Is the coefficient of variation for early Homo closer to the coefficient of variation for chimps or for gorillas?

Exercise 3: Brain Volume Variability

In this section, you will compare the brain volume of apes, hominins, and fully modern humans.Then you will use that data to evaluate the Lump Hypothesis again.

Part 1: Calculate the Difference in Brain Volume and the Index of Dimorphism

Step 1: To determine the difference in mean brain volume for each of the species given in Table 4, subtract the female mean from the male mean. By how many cm³ do the two sexes differ? Write your answers in the chart below.

Step 2: Determine the Index of Dimorphism (I_d) for each species. Remember, the Index of Dimorphism is a relative measure of how different the sexes are for the trait in question. To get this figure, divide the male mean by the female mean. Round off your answer to two decimal places. Write your answer in the chart below.

Step 3: Now consider these statistics for early Homo as a group (Lump Hypothesis) versus Homo habilis separated out and the rest of the early Homo specimens in a second group (Split Hypothesis). Use the descriptive statistics that you calculated in Table 4 to evaluate both hypotheses in the discussion questions below.

Table 4: Brain Volume (c³)

Species	sex	Mean (c3)	M/F Difference (c3)	Index of Dimorphism
Gorilla gorilla	male	535	79	1.17
	female	456
Pongo(Orangutan)	male	434
	female	375
Pan troglodytes(chimp)	male	398
	female	371
Pan paniscus(bonobo)	male	356
	female	329
A. afarensis	male	500
	female	400
A.africanus	male	490
	female	430
P. boisei	male	507
	female	437
Lump Hypothesis
early Homo	male	700
	female	551
Split Hypothesis
H. habilis	male	730
	female	675
Homo species	male	580
	female	510

Part 2: Discussion Questions for Exercise 3: Brain Volume Variability

1. Compare the data from the Great Apes and Australopiths in Table 4. How do the values for hominin brain volume compare with those obtained for the great apes?If you see differences, what might they imply?

1. Compare the Great Apes and Early Homo in Table 4 and look at the part of the table labeled "Lump Hypothesis." Do the statistics seem to support the Lump Hypothesis (pay special attention to the Index of Dimorphism)? Does the pattern of early Homo match that of other hominoids?

1. Look at the data for the "Split Hypothesis" in Table 4. Here early Homo has been divided into two groups. How does this pattern of variability compare with the variability of the grouping in the "Lump Hypothesis" data? Which of the two hypotheses would you consider falsified by the data in this lab?

Exercise 4: Sexually Dimorphic Cranial Features in Apes and early Homo

Part 1: Observations of Skulls

Video:https://screencast-o-matic.com/watch/cYXFoML2EX

In this exercise we will be looking at specific anatomical features on the skulls of a male and female gorilla, and at the early Homo specimens ER 1470 and ER 1813. ER 1470 is the larger specimen.

The traits we are looking at are sexually dimorphic between males and females, focusing upon the supraorbital torus, supraorbital sulcus, the point of origin for the temporalis muscle, and degree of prognathism (see the illustration below). Remember, in sexually dimorphic monkeys and apes, males are always larger with more robust features than females. Therefore, you should expect the specific features we will be looking at to be larger and/or more robust in males than females.

As you saw in Exercise 2 above, if early Homo is one species, it must be a very sexually dimorphic species. If early Homo is all one species, and KNM-ER 1470 is the larger specimen, it is likely to be the male, given the typical pattern of dimorphism among monkeys and apes. KNM-ER 1813, then, would likely be female.But do these two fossils fit the pattern in other features? Let's look at the features listed above, and not just overall size, to further investigate sexual dimorphism in early Homo.

Make the following observations based upon the skulls and record them on Table 5.

Step 1:Compare the male and female gorilla skulls. Identify on both skulls each of the traits listed in the left-hand column of Table 5. Describe for both the female and male gorilla, whether the feature is "more robust" or "less robust".

Task 2:Now look at the same four traits for KNM-ER 1813 and KNM-ER 1470. As before, for each trait identify on Table 5 whether it is "more robust" or "less robust."

Table 5: Sexually Dimorphic Traits

	Male Gorilla	Female Gorilla		ER 1470	ER 1813
supraorbital torus
supraorbital sulcus
temporalis muscle origin
degree of prognathism

Part 2: Discussion Questions for Exercise 4: Sexually Dimorphic Cranial Features

1. Based upon your observations of the gorilla and early Homo skulls, is it likely that KNM-ER 1813 and KNM-ER 1470 are members of the same species? Or are they more likely members of two different species? When you answer this question, discuss the typical primate patterns of sexual dimorphism in body size as well as the origin of the temporalis muscle, the supraorbital torus, the supraorbital sulcus, and the degree of prognathism (difficult to discern from the 3-D images).

Exercise 5: CV/V in hominins including Australopithecus, Paranthropus, and Homo

Researchers recently published an article comparing the cranial capacities of several ancient hominin species in order to better understand where the Dmanisi fossils fit in the hominin taxonomic tree. Using the data presented by the authors, answer the questions below interpreting the CV and V* values for the hominin groups (Rightmire, Margvelashvilli, and Lordkipanidze 2019).

Table 6:Comparison of hominin cranial capacities

Species/Group	N	CV	V*
Dmanisi	5	10.7	11.2
P. boisei	5	4.2	4.4
H. erectus (Java)	10	11.9	12.1
Sima de los Huesos	15	7.8	8.0
H. sapiens	1000s	~13.7

1. Compare the coefficients of variation (CV) and the coefficient of variation adjusted for a small sample size (V*).Considering the values for modern human populations, which includes thousands of individuals, does the data seem to support unequivocally that H. erectus in Java was a separate species from the hominins from Dmanisi?

1. Consider that a large sample size generally leads to more reliable statistics. While scientists would love to have large, robust samples of hominins to use in their analyses, we only have what researchers have discovered in the fossil record. With this understanding, what are some of the potential dangers of having very small sample sizes in your analysis?

Is this correct?