The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45.
The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45. Find the value of x. Hence, find the mode of the above data.
Arranging the given data in ascending order:
42, 43, 44, 44, (2x + 3), 45, 45, 46, 47
Number of terms = 9 (odd)
$\therefore$ Median $=\left(\frac{n+1}{2}\right)^{\text {th }}$ term
$\Rightarrow 45=\left(\frac{9+1}{2}\right)^{\text {th }}$ term
$\Rightarrow 45=(5)^{\text {th }}$ term
$\Rightarrow 45=2 x+3$
$\Rightarrow 2 x=45-3$
$\Rightarrow 2 x=42$
$\Rightarrow x=21$
Hence, the value of x is 21.
Arranging the given data in ascending order:
42, 43, 44, 44, 45, 45, 45, 46, 47
Here, 45 occurs maximum number of times.
∴ Mode = 45
Hence, the mode of the data is 45.
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