Krishna
0

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 40 , and the class corresponding

to  this frequency is 1500 - 2000.

So, the modal class is 1500 - 2000.

lower boundary l = 1500

Class size h = 2000 - 1500 = 500

The frequency of modal class f_1 = 40

The frequency of the class preceding the modal class f_0 = 24

The frequency of the class succeeding the modal class. f_2 = 33

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

= 1500+\frac{40-24}{2*40-24-33}*500

= 1500+\frac{16}{23}*500

= 1500 + 347.826

= 1847.826

Hence, mode = 1847.826

Modal monthly expenditure = 1847.82

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.

Step deviation method

x_i is the class mark = Average of the boundaries(class intervals)

Assumed  value a = middle value of the observations = 2750

Deviation  d_i = x_i - a

Step deviation u_i = \frac{d_i}{h}

h = size of the class = 1500 - 1000= 500

Sum of the values of all the observations  \Sigma f_iu_i=-35

Total number of observations \Sigma f_i=200

Substitute all the values in the values in the step deviation formula

Formula: Mean =   a + \frac{\Sigma f_iu_i}{\Sigma f_i}*h

= 2750 + \frac{-35}{200}*500

= 2750 - 87.5

Mean = 2662.50

Mean of the monthly expenditure = 2662.50