Question

The mean, median and mode respectively of the numbers
7, 4, 3, 5, 6, 3, 3, 2, 4, 3, 4, 3, 3, 4, 4, 3, 2, 2, 4, 3, 5, 4, 3, 4, 3, 4, 3, 1, 2, 3, are _ _ _ _ _ _.
A.3.47, 3, 3
B.3, 3, 3
C.4, 3, 3
D.5, 4, 3

Answer 1

Hint: As we know, the mean is the average of the data. In this question, we need to calculate the mean of random ungrouped data. To calculate the mean of ungrouped data given, we have the formula $\overline x = \dfrac{1}{n}\sum\limits_{i = 1}^n {{x_i}} $ . We have to put the values in the above formula to get the mean value. Now, we need to observe the data whether it has an even or odd number of terms then we will find the middle term of the sorted data. For an odd number of terms, the middle term can simply be calculated by observing the middle term or by adding one to the total number of terms and dividing by 2 and this term will be the median. For even number of terms, there will be two middle terms which is calculated by $\dfrac{n}{2},\dfrac{n}{2} + 1$ and then these two terms can be added and divided by 2 to get the median of data. Now, as we know, mode is the term which has the highest number of frequencies in the given data.

Complete step-by-step answer:
According to the question, number of observations $n = 30$
Now, the sum of all the numbers = 7+4+3+ 5+6+3+3+2+4+3+4+3+3+4+4+3+2+2+4+3+5+4+3+4+3+4+ 3+1+2+3
So, the sum = 104
Using formula for mean, we get:
$
\Rightarrow \bar x = \dfrac{1}{n}\sum\limits_{i = 1}^n {{x_i}} \\
\Rightarrow \bar x = \dfrac{1}{{30}}\sum\limits_{i = 1}^{30} {{x_i}} \\
\Rightarrow \bar x = \dfrac{{104}}{{30}} \\
\Rightarrow \bar x = 3.47 \\
 $
So, the mean is 3.47.
Now, the mode is the number which has the highest frequency.
So, we can see mode is 3.
Now, for median we need to arrange the numbers in ascending order,
1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7
Now, as we know, number of observations are 30
So, using the formula for median of even numbered observation
Now, the middle term is $m = 3$
And the next term to middle term is ${m_1} = 3$
Here, Formula used for median is $\dfrac{{m + {m_1}}}{2}$
Now, substituting the values $m = 3$and ${m_1} = 3$
Median is
$
 = \dfrac{{3 + 3}}{2} \\
  = 3 \\
 $
Hence, median is 3
So the correct option is A.

Note: Attention is needed to do these types of questions because we have to take a lot of values in calculation and we cannot make mistakes in the values. The calculation of mean, median and mode should also be rechecked to avoid any mistakes in these types of questions.