Answer
Verified
376.2k+ views
Hint: To obtain the score of ${{25}^{th}}$ class member we will form two equations. Firstly we will form an equation of mean of 24 test scores by the given data then we will find the equation of mean score of 25 members. Finally we will solve both the equation and subtract the total score before and after ${{25}^{th}}$ member took a test to get our desired answer.
Complete step-by-step solution:
It is given that the mean of 24 test scores is $77.5$.
So let total score of 24 class member is $x$ so we get,
$\dfrac{x}{24}=77.5$
On simplifying we get,
$\begin{align}
& x=77.5\times 24 \\
& \Rightarrow x=1860 \\
\end{align}$…..$\left( 1 \right)$
So total test score of 24 class member is 1860
Next when the ${{25}^{th}}$ class member takes the test the mean goes down by $1.1$ points.
So let new total test score be $y$ so we get,
$\begin{align}
& \dfrac{y}{25}=77.5-1.1 \\
& \Rightarrow \dfrac{y}{25}=76.4 \\
& \Rightarrow y=25\times 76.4 \\
\end{align}$
$\therefore y=1910$….$\left( 2 \right)$
Now to find the test score of ${{25}^{th}}$ class member we will subtract equation (2) by equation (1) as follows:
$\begin{align}
& y-x=1910-1860 \\
& \therefore y-x=50 \\
\end{align}$
So we get that test score of ${{25}^{th}}$ class member is 50.
Hence score of ${{25}^{th}}$ member is 50.
Note: Mean of a list of things is same as the average where we divide the total sum of the data given by the number of data we have. It is a very common term in statistics and used in many areas of mathematics as well. There are many types of mean such as Pythagorean mean, Arithmetic mean, Geometric mean, Harmonic mean etc.
Complete step-by-step solution:
It is given that the mean of 24 test scores is $77.5$.
So let total score of 24 class member is $x$ so we get,
$\dfrac{x}{24}=77.5$
On simplifying we get,
$\begin{align}
& x=77.5\times 24 \\
& \Rightarrow x=1860 \\
\end{align}$…..$\left( 1 \right)$
So total test score of 24 class member is 1860
Next when the ${{25}^{th}}$ class member takes the test the mean goes down by $1.1$ points.
So let new total test score be $y$ so we get,
$\begin{align}
& \dfrac{y}{25}=77.5-1.1 \\
& \Rightarrow \dfrac{y}{25}=76.4 \\
& \Rightarrow y=25\times 76.4 \\
\end{align}$
$\therefore y=1910$….$\left( 2 \right)$
Now to find the test score of ${{25}^{th}}$ class member we will subtract equation (2) by equation (1) as follows:
$\begin{align}
& y-x=1910-1860 \\
& \therefore y-x=50 \\
\end{align}$
So we get that test score of ${{25}^{th}}$ class member is 50.
Hence score of ${{25}^{th}}$ member is 50.
Note: Mean of a list of things is same as the average where we divide the total sum of the data given by the number of data we have. It is a very common term in statistics and used in many areas of mathematics as well. There are many types of mean such as Pythagorean mean, Arithmetic mean, Geometric mean, Harmonic mean etc.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE