Krishna
0

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 10 , and the class corresponding

to this frequency is 30 - 35.

So, the modal class is 30 - 35.

lower boundary l = 30

Class size h = 35 - 30 = 5

The frequency of modal class f_1 = 10

The frequency of the class preceding the modal class f_0 = 9

The frequency of the class succeeding the modal class. f_2 = 3

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

= 30 + \frac{10 - 9}{2*10 - 9 - 3} * 5

= 30 + \frac{1}{8} * 5

= 30 + 0.625

= 30.625

Hence, mode = 30.625.

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 = 32.5

Deviation d_i = x_i - a

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

h = size of the class = 35 - 30= 5

Sum of the values of all the observations \Sigma f_ix_i = -23\Sigma f_iu_i=-23

Total number of observations \Sigma f_i = 35

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

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

= 32.5 + \frac{-23}{35}*5

= 32.5 - \frac{23}{7}

= 29.22

Mean = 29.22