[tex]\large\underline{\sf{Solution-}}[/tex]

Frequency distribution table is as follow :-

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf Class\: interval&\sf Frequency\: (f)&\sf \: cumulative \: frequency\\\frac{\qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad}{}\\\sf 4 - 8&\sf 9&\sf9\\\\\sf 8 - 12 &\sf 16&\sf25\\\\\sf 12-16 &\sf 12&\sf37\\\\\sf 16 - 20&\sf 7&\sf44\\\\\sf 20-24&\sf 15&\sf59\\\\\sf 24-28&\sf 1&\sf60\\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}[/tex]

We know, Median for continuous series is given by

[tex]\boxed{ \sf Median \: = \: l \: + \: \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}} \\ \\ [/tex]

Here,

• l denotes lower limit of median class

• h denotes width of median class

• f denotes frequency of median class

• cf denotes cumulative frequency of the class preceding the median class

• N denotes sum of frequency

[tex] \\[/tex]

From frequency distribution table,

• N = 60

• [tex]\rm \: \dfrac{N}{2} [/tex] = 30

• Median class is 12 - 16

• l = 12,

• h = 4,

• f = 12,

• cf = cf of preceding class = 25

[tex] \\[/tex]

By substituting all the given values in the formula,

[tex]\rm \: Median \: = \: 12 \: + \: \Bigg \{4 \times \dfrac{ \bigg( 30 - 25 \bigg)}{12} \Bigg \} \\ \\ [/tex]

[tex]\rm \: Median \: = \: 12 \: + \: \Bigg \{ \dfrac{5}{3} \Bigg \} \\ \\ [/tex]

[tex]\rm \: Median \: = \: 12 \: + 1.67 \\ \\ [/tex]

[tex]\bf\implies \: Median \: = \: 13.67 \: \: \:(approx.) \\ \\ [/tex]

[tex]\rule{190pt}{2pt} \\ [/tex]

[tex] { \red{ \mathfrak{Additional\:Information}}}[/tex]

1. Mean using Direct Method :-

[tex]\boxed{ \rm{ \:Mean = \dfrac{ \sum f_i x_i}{ \sum f_i} \: }} \\ \\ [/tex]

2. Mean using Short Cut Method :-

[tex]\boxed{ \rm{ \:Mean = A \: + \: \dfrac{ \sum f_i d_i}{ \sum f_i} \: }} \\ \\ [/tex]

3. Mean using Step Deviation Method :-

[tex]\boxed{ \rm{ \:Mean = A \: + \: \dfrac{ \sum f_i u_i}{ \sum f_i} \times h \: }} \\ \\ [/tex]

Answer:

Frequency distribution table is as follow :-

We know, Median for continuous series is given by

Here,

l denotes lower limit of median class

h denotes width of median class

f denotes frequency of median class

cf denotes cumulative frequency of the class preceding the median class

N denotes sum of frequency

From frequency distribution table,

N = 60

= 30

Median class is 12 - 16

l = 12,

h = 4,

f = 12,

cf = cf of preceding class = 25

By substituting all the given values in the formula,

1. Mean using Direct Method :-

2. Mean using Short Cut Method :-

3. Mean using Step Deviation Method :-