Question

The media of a frequency distribution is 89.0 and the first quartile in 75.5. Find the standard deviation by assuming that the distribution is normal.​

Answer 1

Given : The median of a frequency distribution is 89.0 and

the first quartile in 75.5.

To Find :  the standard deviation by assuming that the distribution is normal.​

Solution:

distribution is normal.​

Hence Median = Mean = 89

first quartile in 75.5.

Hence 25 % data lies below 75.5

25% = 0.25   Hence z score is  -0.674

Z score =  ( value - mean ) / SD

-0.674 = ( 75.5 - 89)/SD

=> SD = 13.5/0.674

=> SD = 29.7

standard deviation = 29.7

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