If the values of mean and median are 40 and 48. find out the most probable value of mode.

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Solution

The correct option is A (adsbygoogle = window.adsbygoogle || []).push({}); 30Explanation for the correct answer:Find out the value of empirical mode.Given, mean and median are 36 and 34 respectivelyWe know, Mode=3median-2mean=334-236 =102-72=30Hence, the correct option is A.

If the values of mean and median and mode are x, y & z respectively. Which of these represents the most probable value.

1. x ϵ (y z)
2. z ϵ [x  y)
3. y ϵ [x  z]
4. None of these

Answer (Detailed Solution Below)

Option 3 : y ϵ [x  z]

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Formula used:

Relation b/w mean, mode & median:

Mode = 3 (Median) - 2 (Mean)

Note:  Median always lies b/w mean & mode.

Explanation:

Given,

Mean and median and mode are x, y & z respectively

We know that,

in the case of symmetric distribution, 

Mean = mode = median

When the frequencies are not properly distributed the following empirical relationship holds good given by Karl Pearson and is expressed as

Mode = 3 Median - 2 Mean. 

As median always lies b/w mean & mode.

Hence, option y ϵ [x z] is correct.

When a distribution is symmetrical, the mode, median and mean are all in the middle of the distribution. 

Skewed distributions:

• When the frequencies are not properly distributed it is called an asymmetrical or skewed distribution.
• When a distribution is skewed the mode remains the most commonly occurring value, the median remains the middle value in the distribution.
• The mean is generally ‘pulled’ in the direction of the tails.

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