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Tell whether the statement is true or false:
$(i)$. The mode is always one of the numbers in a data.
$(ii)$. The mean is one of the numbers in a data.
$(iii)$. The median is always one of the numbers in a data.
$(iv)$. The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
To do:
We have to find whether the given statements are true or false.
Solution:
(i) We know that mode is the observations that occur the highest number of times in a given data. Therefore, it is one observation in data.
The given statement is true.
(ii) Mean may or may not be one of the numbers present in a data. It can also be a number that is not a part of the given observations.
The given statement is false.
(iii) Median is the middle observations of the given data when it is arranged in ascending or descending order.
The given statement is true.
(iv) The given data 6, 4, 3, 8, 9, 12, 13, 9.
We know that, Mean$=\frac{ \text { Sum of all the observations }}{ \text { Total number of observations }}$
$=\frac{6+4+3+8+9+12+13+9}{8}$
$=\frac{64}{8}$
$=8$
Therefore, the mean is $8$.
The given statement is false.
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