** MODE: **

Step 1: Recall the mode formula for the grouped data

Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h

l - The lower boundary of the modal class,

h - The class size,

f_1 - The frequency of modal class,

f_0 - the frequency of the class preceding the modal class,

f_2 - the frequency of the class succeeding the modal class.

Step 2: Identify the modal class and locate the values of the frequencies.

NOTE: Locate a class with the maximum frequency, called the modal class.

(The mode is a value inside the modal class)

Here the maximum class frequency is 23, and the class corresponding

to this frequency is 35 - 45.

So, the modal class is 35 - 45.

lower boundary l = 35

Class size h = 45 - 35 = 10

The frequency of modal class f_1 = 23

The frequency of the class preceding the modal class f_0 = 21

The frequency of the class succeeding the modal class. f_2 = 14

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

Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h

= 35 + \frac{23 - 21}{2*23 - 21 - 14} * 10

= 35 + \frac{2}{46 - 35} * 10

= 35 + 1.8181

= 36.8181

Hence, mode = 36.8181

MEAN:

Step 4: Calculate the mean of the given data

Mean: The mean (or average) of observations is the sum of the values of

all the observations divided by the total number of observations.

Sum of the values of all the observations \Sigma f_ix_i = 2830

Total number of observations \Sigma f_i = 80

So, mean = \frac{2830}{80}

Mean = 35.37

Step 5: Compare and interpret the two measures of central tendency.

The mode of the data shows that maximum number of patients is in the

age group of 36.8, while average age of all the patients is 35.37.