Black Bream fish:Statistics Mathematics Assignment

The scientists have collected a number of Black Bream fish. Their lengths have been recorded in the Excel file.

1. State the mean length of Black Bream fish to the nearest centimetre. 1
2. State the median length of Black Bream fish to the nearest centimetre. 1
3. State the range of lengths of Black Bream fish to the nearest centimetre. 1
4. State the standard deviation of the sample of the lengths of Black Bream fish to three decimal places. 1

QUESTION 6(6 marks)

Scientists collected water samples and counted the number of Brine shrimp in each sample.A histogram can be found in the Excel file showing this data.

1. How many samples contained 3 or fewer Brine shrimp? 1
2. What is the modal number of Brine shrimp? 1
3. What is the mean number of Brine shrimp in each sample, to one decimal place? 1
4. Produce a cumulative frequency histogram and polygon (ogive) showing the number of Brine shrimp in each sample. 3

QUESTION 7(4 marks)

A Pareto chart has been partially completed showing the quantities of different species of frogs in the wetlands. The line graph has been completed but the columns are missing.

1. Which species of frog is most common? 1
2. What percentage of frogs were Southern corroboree frogs? 1
3. There were 40 Southern bell frogs. How many frogs were there in total? 1
4. How many Spotted marsh frogs were there? 1

QUESTION 8 (10 marks)

• A number of pelicans were recorded in the study. Their weights are recorded in the Excel file.

1. Complete this two-way table: 2

b.For male pelicans:

• Produce a five-number summary of the data. 2
• Find any outliers, showing all working. 2

• Produce a parallel box plot showing the weights of both the male and female pelicans. Make sure you find all outliers and indicate them on the box plot. 2
• Compare the distribution of weights of male and female pelicans. 2

QUESTION 9(12 marks)

1. In a separate study, scientists collected data on 16 different Green tree frog tadpoles living in captivity. The age (days since hatching) and length of each Green tree frog tadpole has been recorded in the Excel file.
2. Create a scatter plot showing the age and length of Green tree frog tadpoles with the length as the dependent variable. 2
3. State Pearson’s correlation coefficient for the data, correct to three decimal places. 1
4. Describe the strength and direction of the association. 2
5. State the equation of your least-squares regression line of best fit.
   Give your coefficients to 3 decimal places. 2
6. How long would you expect a one-week-old Green tree frog tadpole to be?
   Use your least-squares regression equation to calculate your answer in mm, correct to 1 decimal place. 1
7. Predict the age of a Green tree frog tadpole with a length of 30 mm using your least-squares regression equation. Give your answer to the nearest day. 1
8. The scientists produced a box plot of the lengths of wild Green tree frog tadpoles found in the wetlands. It can be found in the Excel file.
9. What is the median length of wild Green Tree frog tadpoles found in the wetlands? 1
10. A wild Green Tree frog tadpole is in the shortest 25% of wild Green Tree frog tadpoles. What is the shortest it could be and what is the longest it could be? 1
11. A wild Green Tree frog tadpole is longer that 75% of wild Green Tree frog tadpoles.
    Use your least-squares regression equation from part (d) to predict its age to the nearest day.               1

QUESTION 10(4 marks)

1. Scientists have been recording the prevalence of a specific chemical, Bifenthrin, in the Gwydir Wetlands each year. Their records can be found in the Excel file.
2. They know that the prevalence of Bifenthrin is linearly correlated with the prevalence of rotifers, microscopic animals that live in wetlands. They have collected water samples from different wetlands and recorded both the concentration of Bifenthrin and the population density of rotifers. Their results are recorded in the Excel file.
3. Use linear regression to predict the population density of rotifers in the Gwydir Wetlands in the year 2025. Give your answer to the nearest integer in ‘rotifers per Litre’ and show all your working. 4