Question

The following table shows the ages of the patients admitted in a hospital during a year:

Age (in years) 5−15 15−25 25−35 35−45 45−55 55−65
Number of patients 6 11 21 23 14 5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer 1

The mode of the data is 35-45 years, and the mean is 20.4375 years. The mode represents the age group with the highest frequency, while the mean represents the average age of all the patients.

Step-by-step explanation:

To find the mode of the data, we look for the age group with the highest frequency. In this case, the age group with the highest frequency is 35-45, which has 23 patients. Therefore, the mode is 35-45 years.

To find the mean, we multiply each age by its corresponding frequency, sum up the products, and divide by the total number of patients. The calculations are as follows:

(5-15) * 6 + (15-25) * 11 + (25-35) * 21 + (35-45) * 23 + (45-55) * 14 + (55-65) * 5 = 1635

Mean = 1635 / 80 = 20.4375

The mode represents the age group with the highest frequency, while the mean represents the average age of all the patients. In this case, the mode is 35-45 years, and the mean is 20.4375 years. The mode gives us a specific age group that is most common, while the mean gives us the average age of all the patients.