Question

The height of boys and girls of IX class of a school are given below:

Height(cm)	135	140	147	152	155	160
Boys	2	5	12	10	7	1
Girls	1	2	10	5	6	5

Compare the average height of boys and girls.

Answer 1

Hint: First of all, we will find the average (or mean) height of boys and girls separately, and then we compare the average heights of boys and girls. To find the mean height of boys, we will multiply each height with the corresponding number of boys and then add all these multiplications of height and number of boys. After that, we will divide this addition by the total number of boys. Hence, we will get the mean height of boys. Similarly, we can find the mean height for girls.

Complete step-by-step solution:
First of all, we are going to find the average (or mean) height of boys and girls respectively. The mean height of boys is calculated as follows:
Firstly, we are going to multiply each measure of the height with the corresponding boys who have that measure of height. And let us name height as “h” and boys as “b”

Height(cm)(h)	135	140	147	152	155	160
Boys(b)	2	5	12	10	7	1
h(b)	270	700	1764	1520	1085	160
Girls	1	2	10	5	6	5

Now, we are going to add all the multiplications of “h” and “b” we get,
$\begin{align}
  & 270+700+1764+1520+1085+160 \\
 & =5499 \\
\end{align}$
Adding all the number of boys given in the above table we get,
$\begin{align}
  & 2+5+12+10+7+1 \\
 & =37 \\
\end{align}$
Dividing 5499 by 37 we will get the mean height of boys.
$\begin{align}
  & \dfrac{5499}{37} \\
 & =148.62cm \\
\end{align}$
Hence, we got the height of boys as 148.62 cm.
Now, we are going to find the mean height of the girls in the same way in which we have found the height for boys.
Multiplying different measures of height with the corresponding number of girls we get,

Height(cm)(h)	135	140	147	152	155	160
Boys(b)	2	5	12	10	7	1
h(b)	270	700	1764	1520	1085	160
Girls(g)	1	2	10	5	6	5
h(g)	135	280	1470	760	930	800

Now, we are going to add all the multiplications of “h” and “g” we get,
$\begin{align}
  & 135+280+1470+760+930+800 \\
 & =4375 \\
\end{align}$
Adding all the number of girls given in the above table we get,
$\begin{align}
  & 1+2+10+5+6+5 \\
 & =29 \\
\end{align}$
Dividing 4375 by 29 we will get the mean height of boys.
$\begin{align}
  & \dfrac{4375}{29} \\
 & =150.86cm \\
\end{align}$
Hence, we got the mean height of the girls as 150.86 cm.
Now, comparing the average height of girls and boys we get,
The average height of girls is equal to 150.86 cm whereas the average height of boys is equal to 148.62 cm so you can see that the average height of girls is greater than the average height of boys. This means that on average girls are taller than boys.



Note: The mistake that could happen in the above problem is in the wrong multiplication of height with the corresponding number of boys or girls. In the below, we have shown the table given above:

Height(cm)	135	140	147	152	155	160
Boys	2	5	12	10	7	1
Girls	1	2	10	5	6	5

Now, when we multiply the height by the number of boys then you might mistakenly multiply with the number of girls.
For e.g., when we are multiplying say the height of 140 then instead of multiplying with 5 you might have multiplied with 2. This is the error that could be possible so to avoid this mistake make a different table in which you will make a row which lies beneath the boy’s row. In the below table, we have constructed a row, which lies below the rows of boys.

Height(cm)(h)	135	140	147	152	155	160
Boys(b)	2	5	12	10	7	1
h(b)	270	700	1764	1520	1085	160
Girls	1	2	10	5	6	5