Question

. Find the mode of the following data.
(a) 12, 8, 4, 8, 1, 8, 9, 11, 9, 10, 12, 8

Answer 1

Answer:

Given :-

• The data is 12 , 8 , 4 , 8 , 1 , 8 , 9 , 11 , 9 , 10 , 12 , 8

To Find :-

• What is the mode of the following data.

Solution :-

Given Data :

$\mapsto \bf 12 , 8 , 4 , 8 , 1 , 8 , 9 , 11 , 9 , 10 , 12 , 8$

First, we have to arrange the data into ascending order :

$\leadsto \sf 12 , 8 , 4 , 8 , 1 , 8 , 9 , 11 , 9 , 10 , 12, 8$

$\leadsto \sf\bold{\purple{1 , 4 , 8 , 8 , 8 , 8 , 9 , 9 , 10 , 11 , 12 , 12}}$

Now, we have to find that how many times this number occurs :

➳ 1 occurs 1 time

➳ 4 occurs 1 time

➳ 8 occurs 4 time

➳ 9 occurs 2 time

➳ 10 occurs 1 time

➳ 11 occurs 1 time

➳ 12 occurs 2 time

So, here we can notice that 8 occurs maximum number of times i.e, 4 times.

Hence, the mode is 8 .

$\sf\bold{\red{\underline{\therefore\: The\: mode\: is\: 8\: .}}}$

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EXTRA INFORMATION :-

$\clubsuit$ Mean Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: Of\: Observations}{Total\: Number\: Of\: Observations}}}}\: \: \: \bigstar$

$\clubsuit$ Median Formula :

$\bigstar \: \: \sf\boxed{\bold{\red{Median =\: l + \left (\dfrac{\dfrac{n}{2} - cf}{f} \right ) h}}}\: \: \: \bigstar$

where,

• l = Lower Limit of Median Class
• n = Number of Observations
• cf = Cumulative frequency of class preceding the median class
• f = Frequency of Median Class
• h = Class Size (assuming class size to be equal)

$\clubsuit$ Mode Formula :

$\bigstar \: \: \sf\boxed{\bold{\purple{Mode =\: l + \left (\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \right ) h}}}\: \: \: \bigstar$

where,

• l = Lower Limit of the Modal Class
• h = Size of the class interval (assuming all class size to be equal)
• $\sf f_1$ = Frequency of the Modal Class
• $\sf f_0$ = Frequency of the class preceding the Modal Class
• $\sf f_2$ = Frequency of the class succeeding the Modal Class

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Answer 2

Given:

The data or the observations are 12,8,4,8,1,8,9,11,9,10,12,8.

To find out:

Mode of the data.

Solution:

Mode: Mode is the most frequently occurring value of the given data.

The data in ascending order: 1,4,8,8,8,8,9,9,10,11,12,12

In the above given data:

1,4,10 and 11 occurs for once, 8 occurs 4 times, 9 and 12 occurs for twice. So 8 is occurring more times than any other number.

Therefore the mode of the data is 8.

Additional:

Mean: Mean is the average of the given data.

Mean = Sum of Observations/ Number of Observations

Mean = 12+8+4+8+1+8+9+11+9+10+12+8/12

Mean = 100/12

Mean = 8.333333..

Therefore the mean of the data is 8.3333..

Median: Median is the middle number when the data is arranged in ascending or descending order.

The data in descending order: 12,12,11,10,9,9,8,8,8,8,4,1.

The number of observations are 12 and it is even so we should do the average of middle values of the above data.

Median={(n/2)th term + (n/2+1)th term}/2

Median={(12/2)th term + (12/2+1)th term}/2

Median={(6)th term+(7)th term}/2

Median= 9+8/2

Median= 17/2

Median=8.5

Therefore the median of the above given data is 8.5