Math Problem Statement

Use the box-and-whisker plots to compare the noon temperatures of City A and City B and answer the following: (a) Which city had more noon temperatures above 77 °F? (b) Which city had the highest noon temperature? (c) Which city had a larger median noon temperature? (d) Which city had noon temperatures with a larger interquartile range (IQR)?

Solution

Let's analyzeLet's the analyze box the-and-whisker box plots-and for City-wh A andisk City Ber to plots answer the questions to answer the:

  1. ** questionsQuestion (a)::

Which city### ( hada more noon temperatures) above Which city77°F had?**

  • more ** noon temperaturesObservation** above: City A's third quart77ile°F (? upper- part ** ofCity A** the box:) The is box above plot for77°F, indicating more City data A points above extends 77 above°F than City77 B,°F (part whose of the third quartile third and quart theile is below this whisk mark. er ).
  • -Answer: ** CityCity B A had** more: noon temperatures above 77°F.
  1. Question The ( upperb quart):ile Which for City B city does not had the reach highest noon temperature ? 77°F , - so fewer ** pointsObservation**: are The highest data point above (77°Fthe maximum compared) for to City A City is around 95 A. °F-, whereas ** forAnswer City** B it: is around ** 90°F. City - ** AAnswer****: ** had moreCity A noon temperatures** above had the highest noon temperature77.

3°F..

###Question (c (): Which city hadb) a Which city larger had median noon temperature the?

  • highest ** noonObservation temperature**? : The- median ** line forCity City B A appears** to be: around The75°F maximum, value while (end City A of's median is approximately the 80 whisk°F. er ) - Answer: is City around A had90 a larger°F median. noon- temperature **.
  1. QuestionCity (d B): Which city: had The noon maximum temperatures value with ( aend larger inter ofquart theile range whisk (IerQR)?)** is - around ** Observation**:95 The°F IQR. is- the length of ** the boxAnswer (difference: ** between the thirdCity and B first quart had theiles highest noon temperature). City.

A's IQR is wider than that of City B.

  • Answer: City A had a larger IQR.

Would you like further clarification on any of these answers? Here are five questions to deepen your understanding:

  1. What is the significance of the median in a box-and-whisker plot?
  2. How is the interquartile range (IQR) calculated?
  3. Why is it useful to analyze quartiles in data?
  4. What can outliers### in a (c box)-and Which-wh city had a larger median noon temperature? -isk City A: The median (middle line of the boxer) is around 75°F.
  • City B: The median plot is around 70°F.
  • Answer: indicate City A had a larger median noon temperature.

( aboutd) Which city had a dataset noon?

temperatures with5 a. How larger can box-and inter-whiskquarterile plots help range compare the ( distributionI of twoQR datasets?

)? -Tip : BoxCity-and-wh Aisker plots: are great I forQR visualizing ( the spreaddistance, between median, the and out firstliers in and third data, quart helping toile easily) compare distributions appears. to be about 70°F to 80°F, a 10°F range.

  • City B: IQR is from around 62°F to 77°F, a 15°F range.
  • Answer: City B had a larger IQR.

Would you like further explanations or have any questions?

Here are 5 related questions that expand on this topic:

  1. How do you calculate the median from a box-and-whisker plot?
  2. What does the IQR tell you about data spread, and why is it useful?
  3. How can outliers be identified using a box-and-whisker plot?
  4. What information do the whiskers in a box plot represent?
  5. How do box-and-whisker plots differ from other visual data representations like histograms?

Tip: Always check the whisker lengths and outlier points in a box-and-whisker plot to better understand the distribution of the data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Box-and-Whisker Plots
Median
Interquartile Range (IQR)
Data Distribution

Formulas

Interquartile Range (IQR) = Q3 - Q1
Median = Middle value of a data set
Data above a threshold = count values > threshold

Theorems

Box-and-whisker plot properties: Q1, Median, Q3, Whiskers
IQR shows spread of the middle 50% of data

Suitable Grade Level

Grades 6-8