Question

true or false
•the mode is always one of the numbers in a data.
•the data 6,4,3,8,9,12,13,9 has mean 9.
•m=0 is the solution.
•the mean is one of the number in a date.​

Answer 1

SOLUTION

TO CHECK THE STATEMENTS

TRUE / FALSE

1. The mode is always one of the numbers in a data.

2. The data 6,4,3,8,9,12,13,9 has mean 9.

3. The mean is one of the number in a data

CONCEPT TO BE IMPLEMENTED

Mean

In measure of central tendency mean is the most common measure.

For a given set of observations mean is the average value of a group of numbers.

It is obtained by adding up all the observations divide by the number of observations

Mode

For a set of observations mode is defined to be the value ( or values) of the sample ( or samples) which will occur with maximum frequency.

Mean is based on all the observations and if one of the observation is changed, the mean will also change. On the other hand median and mode may remain unchanged even if a number of sample values be changed.

EVALUATION

CHECKING FOR STATEMENT : 1

The mode is always one of the numbers in a data

Since for a set of observations mode is defined to be the value ( or values) of the sample ( or samples) which will occur with maximum frequency

So this statement is FALSE

CHECKING FOR STATEMENT : 2

The data 6,4,3,8,9,12,13,9 has mean 9

The observations are 6,4,3,8,9,12,13,9

Sum of the observations

$= 6 + 4 + 3 + 8 + 9+ 12+ 13 + 9$

$= 64$

Number of observations = 8

Mean

$\displaystyle = \frac{64}{8}$

$= 8$

So this statement is FALSE

CHECKING FOR STATEMENT : 3

The mean is one of the number in a data

Consider a set of 4 observations 1 , 2 , 4 , 5

Then sum of the observations

$= 1 + 2 + 4 + 5$

$= 12$

Total number of observations = 4

Mean

$\displaystyle = \frac{12}{4}$

$= 3$

Now 3 is not a member of the given observations 1 , 2 , 4 , 5

So this statement is FALSE

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