Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

5)Find the mean, median, mode, range, first quartile, third quartile, and the interquartile range for
each data set given. Is the data skewed?
a. 7, 12, 1, 7, 6, 5, 11, 10, 14, 16, 16, 8, 9, 11, 12, 3
b. 85, 105, 95, 90, 115, 10, 8, 7, 5, 9, 10, 7

Sagot :

mhanifa

Answer:

  • See below

Step-by-step explanation:

Definitions

  • 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

Step 1

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

Step 2

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
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.