Question

The ages of $20$ husbands and wives are given below. Form a two-way frequency table showing the relationship between the ages of husbands and wives with the class-intervals $20-25,25-30$ etc.

$\begin{array}{ccc}\text{S.No}& \text{Age of Husband}& \text{Age of Wife}\\ 1& 28& 23\\ 2& 37& 30\\ 3& 42& 40\\ 4& 25& 26\\ 5& 29& 25\\ 6& 47& 31\\ 7& 37& 35\\ 8& 35& 25\\ 9& 23& 21\\ 10& 41& 38\\ 11& 27& 24\\ 12& 39& 34\\ 13& 23& 20\\ 14& 33& 31\\ 15& 36& 29\\ 16& 32& 35\\ 17& 22& 23\\ 18& 29& 27\\ 19& 38& 34\\ 20& 48& 47\end{array}$

Answer 1

Lets write the individual frequencies if class intervals for Age of wives and Age of husbands.

$\begin{array}{ccc}\text{C.I}& \text{Age of wives-Y}& \text{Age of husbands-X}\\ 20-25& 5& 3\\ 25-30& 5& 5\\ 30-35& 5& 2\\ 35-40& 3& 6\\ 40-45& 1& 3\\ 45-50& 1& 1\end{array}$

Procedure:

Step1:

arrange the Class intervals column wise for "Age of Husband $X$" and row wise for "Age of wives $Y$.

Step 2:

Since, there are $3$ husbands and $5$ wives are in the C.I $20-25$.

So, first fill $3$ members in common cell of C.I $20-25$.

the remaining $2$ members fill in the common cell of C.I $X-(25-30)$ and $Y-(20-25)$.

i.e., Frequency of wives and husbands in C.I $20-25$ are $5$ and $3$ respectively.

Step 3:

Move to the C.I $25-30$ for Age of husbands.

There are $5$ husbands in C.I $25-30$, in which $2$ members are already filled.

So, the remaining $3$ members fill in the common cell of C.I $25-30$.

Now, Frequency of husbands for C.I $(25-30)=5$ satisfied.

Step 4:

Number of wives in C.I $25-30$ are $5$.

In which $3$ members already filled.

So, the remaining $2$ members fill in the common cell of C.I $X-(30-35)$ and $Y-(25-30)$

Here, Number of husbands in C.I $30-35$ is also existed.

Step 5:

Number of wives and husbands in class intervals $30-35$ and $35-40$are $5$ and $6$ respectively.

So, fill $5$ members in the common cell of C.I $Y-(30-35)$ and C.I $X-(35-40)$.

i.e., frequency of $30-35$ for wives is filled.

Since, $6$ members in the C.I $35-40$ for husbands.

So, the remaining $1$ person fill in the common cell of $Y-(35-40)$ and $X-(35-40)$

i.e., frequency of $35-40$ for husbands is filled.

Step 6:

There are $3$ wives in C.I $35-40$.

In which already $1$ filled.

So, the remaining $2$ persons fill in the common cell of $Y-(35-40)$ and $X-(40-45)$.

i.e., frequency of $35-40$ for wives is filled.

Step 7:

Since, $3$ husbands are in C.I $40-45$.

In which already $2$ persons are filled.

So, remaining $1$ person fill in the common cell of $X-(40-45)$ and $Y-(40-45)$.

i.e., frequency of $40-45$ for husbands is $3$ and frequency of $40-45$ for wives is $1$ filled.

Step 8:

Since, $1$ husband and $1$ wife in C.I $(45-50)$.

So, fill $1$ in the common cell of $X-(45-50)$ and $Y-(45-50)$.

Hence, required two-way frequency table is formed.