Question

The table lists the world’s 10 largest deserts.

Largest Deserts in the World
Desert	Area (km2)
Sahara (Africa)	8,800,000
Gobi (Asia	1,300,000
Australian Desert (Australia)	1,250,000
Arabian Desert (Asia)	850,000
Kalahari Desert (Africa)	580,000
Chihuahuan Desert (North America)	370,000
Takla Makan Desert (Asia)	320,000
Kara Kum (Asia)	310,000
Namib Desert (Africa)	310,000
Thar Desert (Asia)	260,000

1. What are the mean, median and mode of the areas listed?
2. How many times the size of the Gobi Desert is the Namib Desert?
3. What percentage of the deserts listed are in Asia?
4. What percentage of the total area of the deserts listed is in Asia?

Answer 1

a. Mean = `"Total area of all deserts"/"Number of deserts"`

= `[(8800000 + 1300000 + 1250000 + 850000 + 580000 + 370000 + 320000 + 310000 + 310000 + 260000)/10]`

= `14350000/10`

= 1435000 km²

Median = `((N/2)"th term" + (N/2 + 1)"th term")/2`

= `(10/2 "th term" + (10/2 + 1) "th term")/2`

= `(5"th term" + 6"th term")/2`

= `(580000 + 370000)/2`

= `950000/2`

= 475000 km²  ......[Here, N = 10]

Mode = Most frequent observation

= 310000 km²

b. Let the size of Gobi desert is x times the Namib desert. 

∴  Gobi desert = x × Namib desert

`\implies` 1300000 = x × 310000

`\implies` x = `1300000/310000`

`\implies` x = 4.19

Hence the size of Gobi desert is 4.19 times of Namib desert.

c. Total number of deserts = 10 

Number of deserts in Asia (Gobi, Arabian, Takla Makan, Kara Kum, Thar) = 5

Hence, percentage of deserts in Asia = `5/10 xx 100%` = 50%

d. Total area of all deserts = 14350000 km²  .....[As calculated in part (a)]

Total area of Asia’s deserts = 1300000 + 850000 + 320000 + 310000 + 260000

= 3040000 km²

Hence, percentage of the total area of the deserts listed in Asia

= `"Total area of Asia's deserts"/"Total area of all deserts"`

= `3040000/14350000 xx 100%`

= 21.1%