Answer
Verified
396k+ views
Hint: To solve this question, we will first assume some variable for the sum of the data set and we know that there are 16 observations. We are also given the mean of these observations. We can find the sum of values of observations from the available data. Now, subtract 16 from the total sum of the data set. The total number of observations will also reduce by 1. Then we will add three observations valued 3, 4 and 5 into the data set. The number observations will now increase by 3. Thus, we can find the mean of the new data set.
Complete step-by-step answer:
We know that the mean of a data set is defined as the ratio of the sum of the values of all the values of observations in the data set and the number of data sets.
We are given that the number of observations in our data set is 16 and the mean is also 16.
Now, let the sum of all the observations of the data set be x.
$\begin{align}
& \Rightarrow \dfrac{x}{16}=16 \\
& \Rightarrow x=256 \\
\end{align}$
Thus, the sum of the values of the observations in the original data set is x = 256.
Now, we will delete an observation valued 16. Thus, we have to subtract 16 from the total sum of values and the number of observations will also decrease by 1.
Thus, the total sum of values after observation valued 16 is deleted is (256 – 16) = 240 and the number of observations is 15.
$\begin{align}
& \Rightarrow mean=\dfrac{240}{15} \\
& \Rightarrow mean=16 \\
\end{align}$
Now, it is given that 3 observations valued 3, 4 and 5 are added to the data set.
The total sum of values of observations after 3 observations are added (240 + 3 + 4 + 5) = 252 and number of observations is (15 + 3) = 3.
$\begin{align}
& \Rightarrow mean=\dfrac{252}{18} \\
& \Rightarrow mean=14 \\
\end{align}$
Therefore, the mean of the resultant observations is 14.
So, the correct answer is “Option d”.
Note: In statistics, only mean if affected if the values of the observations change. Median is defined as the central value of the data set and remains the same as long as the number of observations is the same and the central value is not disturbed. Whereas, mode is a value which occurs maximum number of times and hence doesn’t change if any value other than the value which occurs maximum number of times changes.
Complete step-by-step answer:
We know that the mean of a data set is defined as the ratio of the sum of the values of all the values of observations in the data set and the number of data sets.
We are given that the number of observations in our data set is 16 and the mean is also 16.
Now, let the sum of all the observations of the data set be x.
$\begin{align}
& \Rightarrow \dfrac{x}{16}=16 \\
& \Rightarrow x=256 \\
\end{align}$
Thus, the sum of the values of the observations in the original data set is x = 256.
Now, we will delete an observation valued 16. Thus, we have to subtract 16 from the total sum of values and the number of observations will also decrease by 1.
Thus, the total sum of values after observation valued 16 is deleted is (256 – 16) = 240 and the number of observations is 15.
$\begin{align}
& \Rightarrow mean=\dfrac{240}{15} \\
& \Rightarrow mean=16 \\
\end{align}$
Now, it is given that 3 observations valued 3, 4 and 5 are added to the data set.
The total sum of values of observations after 3 observations are added (240 + 3 + 4 + 5) = 252 and number of observations is (15 + 3) = 3.
$\begin{align}
& \Rightarrow mean=\dfrac{252}{18} \\
& \Rightarrow mean=14 \\
\end{align}$
Therefore, the mean of the resultant observations is 14.
So, the correct answer is “Option d”.
Note: In statistics, only mean if affected if the values of the observations change. Median is defined as the central value of the data set and remains the same as long as the number of observations is the same and the central value is not disturbed. Whereas, mode is a value which occurs maximum number of times and hence doesn’t change if any value other than the value which occurs maximum number of times changes.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Two charges are placed at a certain distance apart class 12 physics CBSE
Difference Between Plant Cell and Animal Cell
What organs are located on the left side of your body class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
The planet nearest to earth is A Mercury B Venus C class 6 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is BLO What is the full form of BLO class 8 social science CBSE