There are 10 observations arranged in ascending order as given be… - Vidyadip

Question

There are $10$ observations arranged in ascending order as given below.
$45, 47, 50, 52, JC, JC + 2, 60, 62, 63, 74.$ The median of these observations is $53.$
Find the value of JC. Also find the mean and the mode of the data.

✓

Answer

i. Given data in ascending order:
$45,47, 50, 52, x, JC+2, 60, 62, 63, 74.$
∴ Number of observations $(n) = 10$ (i.e., even)
∴ Median is the average of middle two observations
Here, the 5th and 6th numbers are in the middle position.
$\therefore \quad \text { Median }=\frac{(x)+(x+2)}{2}$
$\therefore \quad 53=\frac{2 x+2}{2}$
$\therefore 106 = 2x + 2$
$\therefore 106 – 2 = 2x$
$\therefore 104 = 2x$
$\therefore x = 52$
$\therefore$ The given data becomes:
$45, 47, 50, 52, 52, 54, 60, 62, 63, 74.$
$\text { ii. Mean }=\frac{\text { The sum of all observations in the data }}{\text { Total number of observations }}$
$=\frac{45+47+50+52+52+54+60+62+63+74}{10}$
$=\frac{559}{10}=55.9$
$\therefore$ The mean of the given data is 55.9.
iii. Given data in ascending order:
$45, 47, 50, 52, 52, 54, 60, 62, 63, 74.$
$\therefore$ The observation repeated maximum number of times $= 52$
$\therefore$ The mode of the given data is $52.$

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