Question

The class marks of a frequency distribution are 6, 10, 14, 18, 22, 26, 30. Find its class size and class intervals.

Answer 1

Hint: We will find the difference between the two class marks distribution to find the class size. Then divide class size by 2 and subtract it from the class mark to calculate the lower limit. Add the class size and lower limit to calculate the upper limit.

Formula Used:
${\rm{Class}}\,{\rm{mark = }}\dfrac{{{\rm{Upper}}\,{\rm{limit + Lower}}\,{\rm{limit}}}}{{\rm{2}}}$
${\rm{Class}}\,{\rm{Size}} = {\rm{Upper}}\,{\rm{limit}} - {\rm{Lower}}\,{\rm{limit}}$

Complete step by step solution:
Find the difference of between 2 consecutive class marks:
The difference between the 2 class marks is $10 - 6 = 14 - 10 = 18 - 14 = 22 - 18 = 26 - 22 = 30 - 26 = 4$
Thus, the class size of the given frequency distribution is 4.
Find the class interval for class mark 6:
Apply the formula of class mark
${\rm{6 = }}\dfrac{{{\rm{Upper}}\,{\rm{limit + Lower}}\,{\rm{limit}}}}{{\rm{2}}}$
$ \Rightarrow 12 = {\rm{Upper}}\,{\rm{limit + Lower}}\,{\rm{limit}}$….(1)
Apply the formula of class size
${\rm{4}} = {\rm{Upper}}\,{\rm{limit}} - {\rm{Lower}}\,{\rm{limit}}$ ….(2)
Add equations (1) and (2)
$2\,{\rm{upper}}\,{\rm{limit}} = 16$
$ \Rightarrow {\rm{upper}}\,{\rm{limit}} = 8$
Substitute the value of upper limit equation (1)
$ \Rightarrow 12 = 8 + {\rm{Lower}}\,{\rm{limit}}$
$ \Rightarrow {\rm{Lower}}\,{\rm{limit}} = 12 - 8 = 4$
Therefore, the lower limit is 4.
Find the class interval for class mark 10:
Apply the formula of class mark
${\rm{10 = }}\dfrac{{{\rm{Upper}}\,{\rm{limit + Lower}}\,{\rm{limit}}}}{{\rm{2}}}$
$ \Rightarrow 20 = {\rm{Upper}}\,{\rm{limit + Lower}}\,{\rm{limit}}$….(1)
Apply the formula of class size
${\rm{4}} = {\rm{Upper}}\,{\rm{limit}} - {\rm{Lower}}\,{\rm{limit}}$ ….(2)
Add equations (1) and (2)
$2\,{\rm{upper}}\,{\rm{limit}} = 24$
$ \Rightarrow {\rm{upper}}\,{\rm{limit}} = 12$
Substitute the value of upper limit equation (1)
$ \Rightarrow 20 = 12 + {\rm{Lower}}\,{\rm{limit}}$
$ \Rightarrow {\rm{Lower}}\,{\rm{limit}} = 8$
Therefore, the lower limit is 8.
Similarly,
For others,
Hence the class intervals are
4 – 8
8 – 12
12 – 16
16 – 20
20 – 24
24 – 28
28 – 32
Thus, the class size of the given frequency distribution is 4.

Note: Do not get confused with the formula of the class mark and class size. The formula of class mark is ${\rm{Class}}\,{\rm{mark = }}\dfrac{{{\rm{Upper}}\,{\rm{limit + Lower}}\,{\rm{limit}}}}{{\rm{2}}}$ and class size is ${\rm{Class}}\,{\rm{Size}} = {\rm{Upper}}\,{\rm{limit}} - {\rm{Lower}}\,{\rm{limit}}$.