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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.

S.NoAge of HusbandAge of Wife128232373034240425265292564731737358352592321104138112724123934132320143331153629163235172223182927193834204847

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Solution

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

C.IAge of wives-YAge of husbands-X20−255325−305530−355235−403640−451345−5011

**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 35−40are 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.

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