Question

The following are the heights in centimetres of the students in class X.
162, 155, 166, 173, 170, 161, 166, 151, 167, 176, 178, 175, 163, 165, 170, 152, 172, 166, 176, 159, 157, 158, 148, 174, 152, 162, 171, 178, 157, 145, 148.
The given data has been grouped into class intervals in the given frequency distribution table.
Fill in the table with the missing frequencies.

$\begin{array}{cc}Classinterval& Frequency\left(f_i\right)\\ 145-150& 3\\ 150-155& 3\\ 155-160& p=----\\ 160-165& q=----\\ 165-170& r=----\\ 170-175& s=----\\ 175-180& 5\end{array}$

• A. p = 6, q = 4, r = 5, s = 6
• B. p = 6, q = 4, r = 4, s = 6
• C. p = 5, q = 4, r = 5, s = 6
• D. p = 6, q = 5, r = 5, s = 6

Answer 1

The correct option is C p = 5, q = 4, r = 5, s = 6

The data provided is:

162, 155, 166, 173, 170, 161, 166, 151, 167, 176, 178, 175, 163, 165, 170, 152, 172, 166, 176, 159, 157, 158, 148, 174, 152, 162, 171, 178, 157, 145, 148.

In the given frequency table the classes are continuous. So, the values that belongs to a class should be greater than or equal to the lower class but should be less than the upper class.
Example: The value 165 will belong to the class 165-170 but not in 160-165.

Counting the number of values present in the range of 155 -160 in the given data, we obtain p = 5.

Similarily, $q=4$
$r=5s=6$