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.

(i) True

The given statement is true.

Since,

We know that,

Mode is termed as that value of observation which occurs for the maximum number of times.

Hence,

Mode will always be the one of the numbers in a data.

Therefore,

The statement is true.

(ii) False

The given statement is false

Since,

We know that,

Mean of a data is calculated as follows:

Mean =

Hence,

Mean may be or may not be one of the numbers in the data.

Therefore,

The statement is false.

(iii) True

The given statement is true.

Since,

We know that,

Median of any data is known as the middle observation when that data is arranged in ascending or descending order.

Hence,

Median is always one of the numbers in a data

Therefore,

The statement is true.

(iv) False

Since,

We know that,

Mean of a data is calculated as follows:

Mean =

=

=

= 8

Hence,

Mean of the given data is 8 and not 9

Therefore,

The statement is false.

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