Author:
Hannah Hynes-Petty
Subject:
Mathematics
Material Type:
Assessment, Homework/Assignment
Level:
High School
Tags:
  • Washington Office of Superintendent of Public Instruction
  • wa-math
    License:
    Creative Commons Attribution
    Language:
    English, Armenian
    Media Formats:
    Downloadable docs

    Education Standards

    OSPI Statistics and Geometry Instructional Task: Age Distribution

    OSPI Statistics and Geometry Instructional Task: Age Distribution

    Overview

    This resource was created by the Washington Office of Superintendent of Public Instruction. 

    Task

    OSPI Statistics and Geometry Instructional Task H

    Statistics and Geometry; Standard S-ID.2, Claim 1; S-ID.3, Claim 1; S-ID.2, Claim 4D; S-ID.3, Claim 1

    Age Distributions

    Random samples of 200 people from Kenya and the United States were taken. A study will compare the age distributions of the two countries. The data collected is represented in the box plots below.

    • What measure would be used to compare the centers of these distributions? Explain your reasoning with numbers and words.
    • Compare the centers of these distributions and interpret the meaning of these in terms of the population samples.
    • Find the interquartile range (IQR) of each sample and explain what a smaller IQR indicates about a country.
    • Compare the first quartile of each sample and interpret the meaning of these in terms of the population samples. 

    Rubric

    Rubric

    Question Number

    Standard/Claim

    Description

    H

    S-ID.2/Claim 1

     S-ID.3/Claim 1

    S-ID.2/Claim 4D

     S-ID.3/Claim

    A 4-point response demonstrates full and complete understanding of the standards and claims by doing all the following:

    • States the median should be used to compare centers.
    • States the samples are skewed.
    • States the median Kenyan age in the sample is slightly less than 20 years and the median age for the US is slightly less than 40 years.
    • States that Kenya has an average sample that is 20 years younger than the US sample, or equivalent.
    • States an IQR for Kenya in the interval [22, 26] years and for the US is in the interval [38, 42] years.
    • States that a smaller IQR means that more of the sample is around the median age.
    • States the first quartile for Kenya is about half of that of the US, or equivalent.

    States the smaller first quartile for Kenya indicates the lowest 25% of the Kenya sample are younger than US’s.

    A 3-point response demonstrates reasonable understanding of the standards and claims by doing six of the following:

    • States the median should be used to compare centers.
    • States the samples are skewed.
    • States the median Kenyan age in the sample is slightly less than 20 years and the median age for the US is slightly less than 40 years.
    • States that Kenya has an average sample that is 20 years younger than the US sample, or equivalent.
    • States an IQR for Kenya in the interval [22, 26] years and for the US is in the interval [38, 42] years.
    • States that a smaller IQR means that more of the sample is around the median age.
    • States the first quartile for Kenya is about half of that of the US, or equivalent.

    States the smaller first quartile for Kenya indicates the lowest 25% of the Kenya sample are younger than US’s.

    A 2-point response demonstrates partial understanding of the standards and claims by doing four of the following:

    • States the median should be used to compare centers.
    • States the samples are skewed.
    • States the median Kenyan age in the sample is slightly less than 20 years and the median age for the US is slightly less than 40 years.
    • States that Kenya has an average sample that is 20 years younger than the US sample, or equivalent.
    • States an IQR for Kenya in the interval [22, 26] years and for the US is in the interval [38, 42] years.
    • States that a smaller IQR means that more of the sample is around the median age.
    • States the first quartile for Kenya is about half of that of the US, or equivalent.

    States the smaller first quartile for Kenya indicates the lowest 25% of the Kenya sample are younger than US’s.

    A 1-point response demonstrates limited understanding of the standards and claims by doing two of the following:

    • States the median should be used to compare centers.
    • States the samples are skewed.
    • States the median Kenyan age in the sample is slightly less than 20 years and the median age for the US is slightly less than 40 years.
    • States that Kenya has an average sample that is 20 years younger than the US sample, or equivalent.
    • States an IQR for Kenya in the interval [22, 26] years and for the US is in the interval [38, 42] years.
    • States that a smaller IQR means that more of the sample is around the median age.
    • States the first quartile for Kenya is about half of that of the US, or equivalent.

    States the smaller first quartile for Kenya indicates the lowest 25% of the Kenya sample are younger than US’s.

    A 0-point response demonstrates almost no understanding of the standards and claims.

     

     

    OSPI Statistics and Geometry Instructional Task H Exemplar

    OSPI Statistics and Geometry Instructional Task H Exemplar

    Statistics and Geometry; Standard S-ID.2, Claim 1; S-ID.3, Claim 1; S-ID.2, Claim 4D; S-ID.3, Claim 1

    Age Distributions


    Random samples of 200 people from Kenya and the United States were taken. A study will compare the age distributions of the two countries. The data collected is represented in the box plots below.

    • What measure would be used to compare the centers of these distributions? Explain your reasoning with numbers and words.
    • Compare the centers of these distributions and interpret the meaning of these in terms of the population samples.
    • Find the interquartile range (IQR) of each sample and explain what a smaller IQR indicates about a country.
    • Compare the first quartile of each sample and interpret the meaning of these in terms of the population samples.
    • Because the Kenya sample is clearly skewed the median should be used to compare the centers. The US sample is slightly skewed.
    • In the Kenya sample, the median is about 18 years of age and the US median is about 38 years of age. Kenya’s sample had 50% of the people who were 20 years younger than in the US sample.
    • The IQR for Kenya is about 32 years – 7 years, or about 25 years. The IQR for the US is about 58 years – 18 years, or about 40 years. A smaller IQR indicates that more of Kenya’s sample is around its median age.
    • The first quartile for Kenya is about 7 years and for the US is about 18 years. This means that youngest 25% of Kenya’s sample is about 11 years younger than the youngest 25% of the US sample.