If the mode of the following data is 14, find the value of x
10,12,14,15,16,14,15,14,15,x,16,14,16

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Solution

The above observation are
10,12,14,15,16,14,15,14,15,x,16,14,16.
Calculating the above observation
x Tally Frequency
10 | 1
12 | 1
14 |||| 4
15 ||| 3
16 ||| 3
By definition, mode is the value that occurs the maximum numbers of times.
from the table we see that 14 occurs maximum numbers of times and it is given that 14 is the mode of the given data.
$∴$ x must be 14 since 15 and 16 occurs thrice are cannot be 15 or 16.
Hence , x=14

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