Comparing and Contrasting Data Distributions

ID: dabon-fimor
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Comparing and Contrasting Data Distributions

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Problem 1

In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each.

Some summary statistics:

ClareLin mean: 2,000 grams mean: 2,000 grams MAD: 275 grams MAD: 225 grams median: 2,000 grams median: 1,950 grams IQR: 500 grams IQR: 350 grams\begin{array}{ll} \text{Clare} & \text{Lin} \\ \boldsymbol{\cdot} \text{ mean: 2,000 grams} & \boldsymbol{\cdot} \text{ mean: 2,000 grams} \\ \boldsymbol{\cdot} \text{ MAD: 275 grams} & \boldsymbol{\cdot} \text{ MAD: 225 grams} \\ \boldsymbol{\cdot} \text{ median: 2,000 grams} & \boldsymbol{\cdot} \text{ median: 1,950 grams} \\ \boldsymbol{\cdot} \text{ IQR: 500 grams} & \boldsymbol{\cdot} \text{ IQR: 350 grams} \end{array}

1) Which student was better at estimating the mass of the objects?

a) Clare was better\text{Clare was better}b) Lin was better\text{Lin was better}c) They were the same\text{They were the same}

2) Explain your reasoning.

Problem 2

3) A reporter counts the number of times a politician talks about jobs in their campaign speeches. What is the MAD of the data represented in the dot plot?

A template for answering this question. Ask your instructor for an alternative.
a) 1.1 mentions\text{1.1 mentions}b) 2 mentions\text{2 mentions}c) 2.5 mentions\text{2.5 mentions}d) 5.5 mentions\text{5.5 mentions}
Problem 3

4) Four amateur miniature golfers attempt to finish 100 holes under par several times. Each round of 100, the number of holes they successfully complete under par is recorded. Due to the presence of extreme values, box plots were determined to be the best representation for the data. List the four box plots in order of variability from least to greatest.

A template for answering this question. Ask your instructor for an alternative.
Problem 4

5) Select all the distribution shapes for which the median could be much less than the mean. Write each corresponding letter in the answer box and separate letters with commas.

a) symmetric \quad \quad b) bell-shaped \quad \quad c) skewed left \quad \quad d) skewed right \quad \quad e) bimodal

Problem 5

6) What is the five-number summary for the data 0, 2, 2, 4, 5, 5, 5, 5, 7, 11?

Show Work

7) When the minimum, 0, is removed from the data set, what is the five-number summary?

Show Work
Problem 6

8) What effect does eliminating the highest value, 180, from the data set have on the mean and median?

25, 50, 50, 60, 70, 85, 85, 90, 90, 180

Problem 7

9) The histogram represents the distribution of the number of seconds it took for each of 50 students to find the answer to a trivia question using the internet. Which interval contains the median?

A template for answering this question. Ask your instructor for an alternative.
a) 0 to 5 seconds\text{0 to 5 seconds}b) 5 to 10 seconds\text{5 to 10 seconds}c) 10 to 15 seconds\text{10 to 15 seconds}d) 15 to 20 seconds\text{15 to 20 seconds}