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saul85 [17]
2 years ago
15

5)Find the mean, median, mode, range, first quartile, third quartile, and the interquartile range for

Mathematics
1 answer:
hammer [34]2 years ago
4 0

Answer:

  • See below

Step-by-step explanation:

<h3>Definitions</h3>
  • Mean - average number
  • Median - the middlepoint of the data set
  • Mode - the most repeated data in the set
  • Range - the difference between the minimum and maximum values of data set
  • First quartile - Q1, the median of the lower half of the data set
  • Third quartile - Q3, the median of the upper half of the data set
  • IQR - the difference of Q3 and Q1
<h3>Step 1</h3>

Put the data in the ascending order

  • a) 1, 3, 5, 6, 7, 7, 8, 9, 10, 11, 11, 12, 12, 14, 16, 16
  • b) 5, 7, 7, 8, 9, 10, 10, 85, 90, 95, 105, 115
<h3>Step 2</h3>

Find all the numbers

a)

  • Mean = (1+3+ 5+ 6+ 7+ 7+ 8+ 9+ 10+ 11+ 11+ 12+ 12+ 14+ 16+ 16)/16 = 9.25
  • Median = (9 + 10)/2 = 9.5
  • Mode = none
  • Range = 16 - 1 = 15
  • Q1 = (6 + 7)/2 = 6.5
  • Q3 = 12
  • IQR = 12 - 6.5 = 5.5
  • The data is almost uniform as the mean and median are very close

b)

  • Mean = (5+ 7+ 7+ 8+ 9+ 10+ 10+ 85+ 90+ 95+ 105+ 115)/12 = 45.5
  • Median = 10
  • Mode = none
  • Range = 115 - 5 = 110
  • Q1 = (7 + 8)/2 = 7.5
  • Q3 = (90 + 95)/2 = 92.5
  • IQR = 92.5 - 7.5 = 85
  • The data is skewed left as the mean and median are too differenet
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Notice that

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