Question

Given government debt of 16 countries in USD million: 150,80,100,40,210,140,110,95,150,120,150,100,150,60,80,175. How do the following occurrences affect mean, median, mode, range, variance, standard deviation?
(a) a debt penalty of 5% applied to each country
(b) a revision in the debt figure of the most indebted country from USD 210 million to USD 180 million

Answer 1

Debts arranged in ascending order

40

60

80

80

95

100

100

110

120

140

150

150

150

150

175

210

Mean = 119.375,

Median = (110+120) = 115

Mode = 150

Range = 210-40 = 170

Variance = 1865.234

Sd = 43.18836

a)

debt penalty of 5% applied on each country, meaning every value is increased by 5% of each value

So, the new data set would be

42

63

84

84

99.75

105

105

115.5

126

147

157.5

157.5

157.5

157.5

183.75

220.5

Mean = 125.344 (5% increased )

Median = 120.75 (5% increased)

Mode = 157.5 (5% increased)

Range = 178.5 (5% increased)

Variance = 2056.421

Sd = 45.34778 (5% increased)

So, except variance, everything is also increased by 5%

b)

• Median (115) and mode (150) would remain the same
• Mean would reduce by 30/16. So mean = 119.375 - (30/16) = 117.5
• Range would decrease by 30, Range = 170-30 = 140
• Variance and standard deviation will also reduce
• Variance = 1578.125
• Sd = 39.72562