Question

The numbers 52, 53, 54, 54, ( 2 X + 1) 55, 55, 56, 57, have been arranged in an ascending order and the median is 55 find the value of x and hence find the mode of the given

Answer 1

Answer:

Step-by-step explanation:

(N+1/2)=55

(9+1/2)=55

(10/2)=55

5th term=55

2x+1=55

2x=54

X=27

Answer 2

The value of x is 27.

The mode of the give data is 55.

Explanation:

The median is the middlemost value in an well ordered data .

Given : The numbers 52, 53, 54, 54, ( 2 X + 1) 55, 55, 56, 57, have been arranged in an ascending order .

The number of data values = 9 ( odd)

So the median of data = middlemost value = 2 X + 1

Since the median is 55.

⇒ 2x +1 = 55

⇒ 2x= 54  [Subtract 1 from both sides]

⇒x = 27  [Divide both sides by 2]

Hence, the value of x is 27.

After filling the position of 2x+1 by 55 , the complete well ordered data becomes :52, 53, 54, 54,55, 55, 55, 56, 57

Since Mode = Most repeated value = 55

Hence, the mode of the give data is 55.

# Learn more :

The relationship between mean, median and mode for a moderately skewed distribution is

(a)Mode = 2 Median − 3 Mean

(b)Mode = Median − 2 Mean

(c)Mode = 2 Median − Mean

(d)Mode = 3 Median −2 Mean

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