Question

The marks (out of 10) obtained by 28 students in a Mathematics test are listed below:
$8,1,2,6,5,5,5,0,1,9,7,8,0,5,8,3,0,8,10,10,3,4,8,7,8,9,2,0$
The number of students who obtained marks more than or equal to 5 is
A. 13
B. 15
C. 16
D. 17

Answer 1

Hint: We will first arrange it in the form of a table and note down the different values and their frequencies to make a frequency table. Out of these, add the frequency of marks greater than or equal to 5 to get the total number of students who obtained marks more than or equal to 5.

Complete step-by-step solution:
We will represent the frequencies of these values in the table below to help solve them easily. Also, we will arrange these values in ascending order to further ease the question.
In statistics, a frequency distribution/table is a list, table, or graph that displays the frequencies of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a practical group or interval. A frequency distribution shows us a summarized group of data divided into mutually exclusive classes and the number of occurrences in a class.
The frequency of each value is found out by counting the number of times a particular value has been repeated.

Marks	0	1	2	3	4	5	6	7	8	9	10
Frequency	4	2	2	2	1	4	1	2	6	2	2

Now add the frequencies of the marks greater than or equal to 5.
$ \Rightarrow $ Number of students $ = 4 + 1 + 2 + 6 + 2 + 2$
Add the numbers on the right side,
$ \Rightarrow $ Number of students $ = 17$
Thus, the number of students who obtained marks greater than or equal to 5 is 17.
Hence option (D) is correct.

Note: Please keep in mind that the term 'frequency' denotes the number of times an observation appears or occurs in a dataset. Hence, it is quite evident that the frequency shall increase in the case of repetitions. It is imperative to note that the sum of the frequencies should be equal to the total number of observations in the dataset.