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ariel is studying to become a meteorologist. each day last week, she me…

Question

ariel is studying to become a meteorologist. each day last week, she measured the top wind speed in each of three towns near where she lives. the table shows the results. based on the data in the table, what can you conclude about the top wind speeds in these towns over the past week? select all that apply. hillview has the smallest interquartile range. so, hillview had the least variation in top wind speed last week. prairie citys interquartile range is larger than cedar lakes interquartile range. so, prairie city had more variation in top wind speed last week than cedar lake. prairie city has the largest interquartile range. so, prairie city had the most variation in top wind speed last week. cedar lakes interquartile range is larger than hillviews interquartile range. so, cedar lake had more variation in top wind speed last week than hillview.

Explanation:

Step1: Arrange the data in ascending order

  • Hillview: \(12,15,15,18,20,22,25\)
  • Prairie City: \(20,25,25,28,35,37,40\)
  • Cedar Lake: \(5,10,12,20,22,28,30\)

Step2: Find the median (Q2)

  • For Hillview (\(n = 7\)), \(Q2=\frac{(n + 1)}{2}\)th value \(=4\)th value \(=18\)
  • For Prairie City (\(n = 7\)), \(Q2 = 4\)th value \(=28\)
  • For Cedar Lake (\(n = 7\)), \(Q2=4\)th value \(=20\)

Step3: Find Q1 and Q3

  • For Hillview: \(Q1=\frac{15 + 15}{2}=15\), \(Q3=\frac{22+25}{2}=23.5\)
  • For Prairie City: \(Q1=\frac{25+25}{2}=25\), \(Q3=\frac{37 + 40}{2}=38.5\)
  • For Cedar Lake: \(Q1=\frac{10+12}{2}=11\), \(Q3=\frac{28+30}{2}=29\)

Step4: Calculate the inter - quartile range (IQR)

  • \(IQR=Q3 - Q1\)
  • Hillview: \(IQR = 23.5-15 = 8.5\)
  • Prairie City: \(IQR=38.5 - 25=13.5\)
  • Cedar Lake: \(IQR=29 - 11 = 18\)

Answer:

  • Hillview has the smallest interquartile range. So, Hillview had the least variation in top wind speed last week.
  • Prairie City's interquartile range is larger than Cedar Lake's interquartile range. So, Prairie City had more variation in top wind speed last week than Cedar Lake.
  • Prairie City has the largest interquartile range. So, Prairie City had the most variation in top wind speed last week.
  • Cedar Lake's interquartile range is larger than Hillview's interquartile range. So, Cedar Lake had more variation in top wind speed last week than Hillview.