Question

What is the mode of the data given below? [Give your answer correct to 2 decimal places.]

Age in years	15-25	25-35	35-45	45-55	55-65	65-75	75-85
No. of patients	14	32	39	38	10	36	22

• A. 60.47
• B. 36,08
• C. 40.86
• D. 43,75

Answer 1

Answer: (D)

43.75

Answer 2

To find the mode of the given grouped data, we use the formula:

Mode = $l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$

Where:

• $l$ = lower limit of the modal class
• $h$ = size of the class interval
• $f_1$ = frequency of the modal class
• $f_0$ = frequency of the class preceding the modal class
• $f_2$ = frequency of the class succeeding the modal class

Step 1: Identify the modal class.

The modal class is the class interval with the highest frequency. From the given data:

Age in years	No. of patients (Frequency)
15-25	14
25-35	32
35-45	39
45-55	38
55-65	10
65-75	36
75-85	22

The highest frequency is 39, which corresponds to the class interval 35-45. Therefore, the modal class is 35-45.

Step 2: Extract the values for the formula.

• Lower limit of the modal class ($l$) = 35
• Class size ($h$) = Upper limit - Lower limit = 45 - 35 = 10
• Frequency of the modal class ($f_1$) = 39
• Frequency of the class preceding the modal class ($f_0$) = 32 (frequency of 25-35)
• Frequency of the class succeeding the modal class ($f_2$) = 38 (frequency of 45-55)

Step 3: Substitute the values into the mode formula and calculate.

Mode = $35 + \left( \frac{39 - 32}{2(39) - 32 - 38} \right) \times 10$

Mode = $35 + \left( \frac{7}{78 - 70} \right) \times 10$

Mode = $35 + \left( \frac{7}{8} \right) \times 10$

Mode = $35 + \frac{70}{8}$

Mode = $35 + 8.75$

Mode = $43.75$

The mode of the data is 43.75.