Question

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

Answer 1

• See below

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