Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Formula Booklet
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AIHL
    /
    Descriptive Statistics
    /

    Problem Bank

    [Maximum mark: 11]

    Dr. Darwin is interested in studying turtle hatching on a chain of 3 islands, Sandy, Blue and Eagle. Dr. Darwin first wants to estimate the total number of nests on the island chain. To do this, he first finds the total surface area of the islands, ​22km2. He lands his boat on the sheltered side of the largest island, and draws a ​100m​ by ​100m​ square in the sand starting from the point he came ashore. He then counts the number of nests inside the square, and finds ​8.

    1. State

      1. the type of variable being recorded,

        [1]

        To earn a crown, get your answer ready before you reveal the options!

      2. the name of this type of sampling technique.

        [1]
    2. Give two reasons Darwin's measurement is unlikely to produce a reliable estimate of the total number of nests.

      [2]

    Dr. Darwin makes a second attempt at data collection. This time, he visits each island, and takes 4 separate ​100m×100m​ samples, one on each side (north, west, south & east) of the island. The data for the number of nests found in each sample are provided in the table below.

    Island

    North

    West

    South

    East

    Sandy

    7

    4

    8

    7

    Blue

    6

    3

    7

    8

    Eagle

    3

    2

    3

    2

      1. State the name of this type of sampling technique.

        [1]
      2. Using the data collected, estimate the total number of nests across the island chain.

        [2]

    Sandy & Blue both have a surface area of ​9km.

    1. Find the surface area of Eagle Island.

      [1]
      1. Explain why the estimate found in (c.iii) is unlikely to be accurate.

        [1]
      2. Using the same data as in (b.iii), give a revised estimate, to the nearest hundred, for the total number of nests across the island chain.

        [2]

    Ask Plex AI about this problem

    Get hints, ask questions, and work through this problem step by step

    I'm Plex, here to help with problems on this worksheet!