Question

Largest Deserts in the World along with their areas are listed below.

Desert	Area ${km}^{2}$
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)	\[370,000\]
TaklaMakan Desert (Asia)	\[320,000\]
Kara Kum (Asia)	\[310,000\]
Namib Desert (Africa)	\[310,000\]
Thar Desert (Asia)	\[260,000\]

The above table lists the world's $10$ largest deserts.
(a) What is the mean, median and mode of the areas listed ?
(b) How many times the size of the Gobi Desert is the Namib Desert ?
(c) What Percentage of the deserts listed are in Asia ?
(d) What percentage of the total area of the deserts listed is in Asia ?

Answer 1

Hint: For (a), we will use the mean, median and mode formula respectively. In (b), we will find the factor by which the size of the Gobi Desert varies from the Namib Desert. In (c), we will divide the number of deserts in Asia by the total number of deserts given and multiply by $100$ to find the percentage. And in (d), we will add the areas of deserts in Asia and divide it by the areas of all deserts given and multiply by $100$ to find the percentage.

Complete step-by-step solution:
There is total $10$ deserts in the given data
(a) The mean is the sum of all the areas of deserts divided by the number of deserts.
The formula of mean is
$mean = \dfrac{{are{a_1} + are{a_2} + ... + are{a_{10}}}}{{no.of{\text{ }}deserts}}$
Substituting the value of areas in the formula we get,
$mean = \dfrac{{8,800,000 + 1,300,000 + 1,250,000 + 850,000 + 580,000 + 370,000 + 320,000 + 310,000 + 310,000 + 260,000}}{{10}}$
After adding all the values, we get,
\[mean = \dfrac{{{\text{1,43,50,000}}}}{{10}}\] = $1,435,000$
Therefore, the mean of the areas of deserts is $1,435,000{km}^{2}$.
The median is the middle value of a data set. Here, the median will be the middle value of the area.
The formula of median is
\[{\mathbf{Median}}\;{\text{ }} = {\text{ }}\dfrac{{{{\left( {{\mathbf{n}}/{\mathbf{2}}} \right)}^{{\mathbf{th}}}}\;{\mathbf{term}}{\text{ }} + {\text{ }}{{\left\{ {\left( {{\mathbf{n}}/{\mathbf{2}}} \right) + {\mathbf{1}}} \right\}}^{{\mathbf{th}}}}}}{2}\]
Here n = $10$ i.e., the number of deserts
\[{\mathbf{Median}}\;{\text{ }} = {\text{ }}\dfrac{{{{\left( {10/{\mathbf{2}}} \right)}^{{\mathbf{th}}}}\;{\mathbf{term}}{\text{ }} + {\text{ }}{{\left\{ {\left( {10/{\mathbf{2}}} \right) + {\mathbf{1}}} \right\}}^{{\mathbf{th}}}}}}{2}\]
Dividing the value,
\[{\mathbf{Median}}\;{\text{ }} = {\text{ }}\dfrac{{{5^{{\mathbf{th}}}}\;{\mathbf{term}}{\text{ }} + {\text{ }}{{\text{6}}^{{\mathbf{th}}}}{\mathbf{term}}}}{2}\]
Here the ${5^{th}}term = 580,000$ and ${6^{th}}term = 370,000$, substituting these values ,
\[{\mathbf{Median}}\;{\text{ }} = {\text{ }}\dfrac{{580,000 + 370,000}}{2}\]
Adding the numbers,
\[{\mathbf{Median}}\;{\text{ }} = {\text{ }}\dfrac{{950000}}{2}\]
Dividing the number,
\[{\mathbf{Median}}\;{\text{ }} = {\text{ }}475,000\]
Therefore, the median of the areas is \[475,000\]${km}^{2}$ .
Mode is the most frequently occurring value in a data set.
Here, the area of Kara Kum (Asia) and Namib Desert (Africa) is $310,000$ ${km}^{2}$ and it's occurring twice.
Therefore, the mode of areas is $310,000{km}^{2}$.
(b) The area of Namib Desert is $310,000{km}^{2}$ and the size of Gobi Desert (Asia) is \[1,300,000\]${km}^{2}$.
The area of Gobi Desert is more than that of Namib desert. So, if we divide the area of Gobi Desert by Namib desert, we will get the number of times the area of Gobi Desert is more than that of Namib desert.
Let the factor be $x$.
$x = \dfrac{{1300000}}{{310000}}$
Dividing the areas,
$x = 4.19$
Therefore, Gobi Desert is $4.19$ times bigger than Namib desert.
(c) The total number of deserts given is $10$ out of which $5$ are in Asia.
To find the percentage of deserts present in Asia, we use the formula,
$\text{Percentage} = \dfrac{\text{no.of deserts in Asia}}{\text{total no. of deserts}} \times 100$
Substituting the values,
$\text{Percentage} = \dfrac{5}{{10}} \times 100$
Canceling the zeros,
$\text{Percentage}= 5 \times 10$
Multiplying the number,
$\text{Percentage} = 50\% $
Therefore, from the list of $10$ deserts, $50\% $ deserts are in Asia.
(d) The percentage of areas of deserts present in Asia is given by the sum of areas of deserts in Asia divided by the total area of all the deserts and multiplied by $100$.
The total area of deserts is = $8,800,000 + 1,300,000 + 1,250,000 + 850,000 + 580,000 + 370,000 + 320,000 + 310,000 + 310,000 + 260,000$
$ = 14,350,000$ ${km}^{2}$.
The sum of areas of deserts in Asia = $1300000 + 850000 + 320000 + 310000 + 260000 = {\text{30,40,000}}$ km2.
The percentage of area of deserts in Asia
= $\dfrac{{3040000}}{{14350000}} \times 100$
Canceling the zeros,
= $\dfrac{{304}}{{1435}} \times 100$
Dividing the terms,
= $0.2118 \times 100$
Multiplying the terms,
= $21.18\% $
Therefore, the $21.18\% $ of the area of deserts is present in Asia.

Note: We have to be careful while doing operations on large numbers with many zeros. Properly count all the zeros present and do the operation otherwise all the further calculations may go wrong. Here the question comprises the concept of measure of central tendency (mean, mode, median) and percentage, so for solving this problem we have to have a strong knowledge of the formulas and concepts.