Question

Following is data from a child-care center find the mode of data

Age Group	0-2	2-4	4-6	6-8	8-10
Number of children	5	7	3	2	2

• A. 2
• B. 7
• C. 2.67
• D. 3.5

Answer 1

The Correct Option is C

To find the mode, we look for the class with the highest frequency. Here, the age group 2-4 has the highest frequency, with 7 children. Thus, the mode class is 2-4. To calculate the mode, we use the following formula: \[ \text{Mode} = L + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times h \] where:
\( L \) is the lower boundary of the modal class (2),
\( f_1 \) is the frequency of the modal class (7),
\( f_0 \) is the frequency of the class before the modal class (5),
\( f_2 \) is the frequency of the class after the modal class (3),
\( h \) is the class width (2).
Substitute the values: \[ \text{Mode} = 2 + \frac{(7 - 5)}{(2 \times 7 - 5 - 3)} \times 2 = 2 + \frac{2}{6} \times 2 = 2 + \frac{4}{6} = 2.67 \]

The correct option is (C): \(2.67\)