Question

in a perfectly symmetrical distribution the mode and the mean are 42 and 49 respectively approximate median and distribution is _a) 47. b)48. c)49. d)50

Answer 1

we know,
$\boxed{\boxed{\text{mode}\pm2\text{mean}=3\text{median}}}$

Given in a perfectly symmetrical distribution,
the mode = 42
and the mean = 49
we have to find approximate value of the median.
so, $\text{mode}\pm2\text{mean}=3\text{median}$

42 ± 2 × 49 = 3 × median

42 - 2 × 49 = 3 × median [ ignored ]

=> 42 + 2 × 49 = 3 × median

=> 42 + 98 = 3 × Median

=> 140/3 = median

median = 46.67 ≈ 47

hence, answer is option (a).

Answer 2

Given ,

Mode = 42 ,

Mean = 49 ,

Median = ?

By Empharical Formula ,

Mode = 3×median - 2×mean

42 = 3 × median - 2 × 49

=> 42 = 3 × median - 98

=> 42 + 98 = 3 × median

=> 140 = 3 × median

=> Median = 140/3

Medain = 46.666...

≈ 47

Option ( A ) is correct.

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