 Krishna
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Step 1:  Find the median of the given data

Skill 1: Set up a cumulative frequency distribution table

NOTE: The cumulative frequency is calculated using a frequency

distribution table. Skill 2: Calculate the median class of the data.

NOTE: Locate the class whose cumulative frequency exceeds

\frac{n}{2}   for the first time. This is called the median class.

The total number of observations n = 68. So, \frac{n}{2} = 34

125 - 145 is the class whose cumulative frequency is 42 greater than

(and nearest to) \frac{n}{2}, i.e., 25.5.

Therefore, 125 - 145 is the median class

Skill 3: Substitute that values in the median formula

From the table;

l = lower boundary of median class = 125,

n = number of observations = 68,

cf = cumulative frequency of class preceding the median class =13

f = frequency of median class = 20

h = class size (size of the median class) = 145 - 125 = 20.

Substituting the values

Median=l+\frac{\frac{n}{2}-cf}{f}*h

Median = 125 + \frac{34 - 22}{20}*20

= 125 + 12

= 137

Hence, the median = 137

Step 2: Find the mode of the given data

Skill 1: 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 20 , and the class corresponding

to this frequency is 125 - 145.

So, the modal class is 125 - 145.

lower boundary l = 125

Class size        h = 145 - 125 =20

The frequency of modal class f_1 = 20

The frequency of the class preceding the modal class     f_0 = 13

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

Skill 2: Substitute the values in the formula and calculate the mode.

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

= 125 + \frac{20 - 13}{2*20 - 13 - 14} * 20

= 125 + \frac{7}{13} * 20

= 125 + 10.77

= 135.77

Hence, mode = 135.77

Step 3: Calculate the mean of the given data

Skill 1: Choose one among the observations as the assumed mean, and

Find the deviation and step deviation of ‘a’ from each of the observations

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 = 135

Deviation d_i = x_i - a

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

h = size of the class = 85 - 65 = 20

Sum of the values of all the observations \Sigma f_iu_i = 7

Total number of observations \Sigma f_i = 68

Skill 2:  Substitute all the values in the values in the step deviation formula

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

= 135 + \frac{7}{68}*20

= 135 - \frac{140}{68}

= 135 + 2.05

Hence, Mean = 137.05

Step 4: Compare the mean, mode and median

Mean = 137.05, mode = 135.77  median = 137

Mean, mode and median are almost similar