StatisticsBy Varsha Udayakumar

Research in Ecology

Sharp-nosed Sharks

Male Female920

930

940

950

960

970

980

990

1000

Average Length of Sharp-nosed Sharks

Gender of Sharks

Len

gth

(m

m)

Males Females920 840928 850935 932943 960950 960950 965954 972960 980962 980974 985975 995975 1000

1000952.1667 1009

1010952 1010

10101020102510251028103010381043105410601160

997.8148

1009

Male Female952 998

Turtles

BlueYellow

GreenRed

Orange

0

5

10

15

20

25

Site C: Turtle Hatchling Data

Color

# o

f h

atc

hlin

gs

# Hatch-

lings

Sur-

vived

Bottle Caps

Color # of CapsRed 11Orange 4Yellow 9Blue 11Green 9Black 8White 17Clear 8

Sea Cigars(seed propagules)

"1-5" "6-10" "11-15" "16-20" "21-25" "26-30"0123456789

Frequency Distribution of Sea Cigars by Size

Size Intervals (in cm)

No

. o

f S

ea

Cig

ars

Size Interval (cm) No. of sea cigars"1-5" 0

"6-10" 2"11-15" 4"16-20" 9"21-25" 7"26-30" 2

Seed # Length(centimeters)1 92 103 124 135 136 157 168 189 19

10 1911 1912 2013 2014 2015 2016 2017 2118 2119 2220 2321 2522 2523 2524 2625 27

Mean: 19.12Median: 20

Mode: 20Biggest #: 27Smallest#: 9

Range: 18

Coral Planula

Trial # Water Temp. Depth Wave Action Survived?1 1 3 6 No2 1 5 6 No3 2 6 1 No4 1 6 3 No5 2 1 2 No6 4 5 1 No7 2 6 5 No8 4 5 1 No9 3 1 6 Yes10 3 3 6 Yes11 1 1 6 No12 3 1 6 Yes13 3 2 6 Yes14 1 6 4 No15 4 6 6 No16 2 2 6 Yes17 5 5 4 No18 3 4 3 No

Predicted Probability Observed Probabilty0.22 0.28

Probability: a way to measure the chances that something will occur in relation to the possible alternatives

0 0.05 0.1 0.15 0.2 0.25 0.3

Coral Planula Survival Probability

Probability

Typ

e o

f co

ral Observed Probabil-

ity

Predicted Probability

To survive a coral planula needs:

Warm temperatures (but not too warm)Shallow water andRough waves

Variance of Sea CigarsSeed # Length(centimeters)

1 92 103 124 135 136 157 168 189 1910 1911 1912 2013 2014 2015 2016 2017 2118 2119 2220 2321 2522 2523 2524 2625 27

Variance: how much variation exists around the mean.

The Variance formula is:

2= ∑ (X-X)2

n-1

The variance for this data set is

24.44333.

Key:σ2 : the variance n : the number of values

∑ : the sum of

X : the mean

X : each data value

Standard Deviation of Sea CigarsStandard Deviation: describes how spread out the data are; is symbolized σ.

To find the standard deviation:√variance

The standard deviation for

this data set is ±4.94402.

Key:

√ : the square root of

± : plus or minus

Distribution of Sea Cigars

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230

0.5

1

1.5

2

2.5

3

3.5

4

Actual Distribution of Sea Cigars by Length

Length of Sea Cigar (in cm)

Fre

qu

en

cy

Theoretical Distribution Curve: a theoretical or ideal picture of a distribution based upon random sampling

4 6 8 10 12 14 16 18 20 22 240

0.5

1

1.5

2

2.5

3

Theoretical Distribution of Sea Cigars by Length

Length of Sea Cigar (in cm)

Fre

qu

en

cy

T-Test of Painted Lady Butterflies

T-test: meant to test whether there is a significant difference between the means of two independent samples (the difference is also known as the t-statistic).To find the t-statistic:

t = (X1 – X2)

√ sp2 ( + )

Note: The p-value must be less than 0.05 in order to reject the null hypothesis.

Key:X1 : mean of first group sp

2 : the pooled variance

X2 : mean of second group t : the t-statistic

n1 : number of ? used in the first group

n2 : number of ? used in the second group