Compute mode from the following data. Class interval 10 20 20 30 30 40 40 50 50 60 60 70 : : : : : : : Frequency 4 6 8 12 7 3

To compute the mode from the given grouped data, we use the formula for the mode of a grouped frequency distribution:

$$\text{Mode}=L+\left(\frac{f_m-f_1}{(f_m-f_1)+(f_m-f_2)}\right)\times h$$

Where:

• $L$ = Lower limit of the modal class (the class with the highest frequency).
• $f_m$ = Frequency of the modal class.
• $f_1$ = Frequency of the class preceding the modal class.
• $f_2$ = Frequency of the class succeeding the modal class.
• $h$ = Width of the class interval.

Step 1: Identify the Modal Class

From the given data:

The highest frequency is 12, which corresponds to the class 40-50. Thus, the modal class is 40-50.

Step 2: Extract Required Values

• $L=40$ (lower limit of the modal class)
• $f_m=12$ (frequency of the modal class)
• $f_1=8$ (frequency of the class preceding the modal class, i.e., 30-40)
• $f_2=7$ (frequency of the class succeeding the modal class, i.e., 50-60)
• $h=10$ (class width, since each class interval spans 10 units)

Step 3: Apply the Mode Formula

Substitute the values into the formula:

$$\text{Mode}=40+\left(\frac{12-8}{(12-8)+(12-7)}\right)\times 10$$

$$=40+\left(\frac{4}{4+5}\right)\times 10$$

$$=40+\left(\frac{4}{9}\right)\times 10$$

$$=40+\frac{40}{9}$$

$$=40+4.44$$

$$=44.44$$

Final Answer

The mode of the given data is 44.44.