Question

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

Answer 1

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