Which of the following statements is true for the following data set? 7, 5, 6, 4, 7, 8, 12(i) Only the mean and median are equal.(ii) Only the mean and mode are equal.(iii) Only the median and mode are equal.(iv) The mean, median, and mode are all equal.

Solution:

Option (iv) is the correct answer.

Mean:

Let the given observation be denoted by X.

⇒ X ; 7, 5, 6, 4, 7, 8, 12

Now, ∑X = 49

Arithmetic mean, [latex]\overline{X}[/latex]

= 49/7 = 7

Median:

Let the given observation be denoted by X.

Now, arranging the observation in ascending order,

X; 4, 5, 6, 7, 7, 8, 12

Median = ((n + 1) / 2)^th value, because n is odd.

⇒ 4^th value

Therefore,

Median = 7

Mode:

We find that the value ‘7’ appears more time than any of the other data values.

Therefore,

Mode = 7

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Which of the following statements is true for the following data set? 7, 5, 6, 4, 7, 8, 12(i) Only the mean and median are equal.(ii) Only the mean and mode are equal.(iii) Only the median and mode are equal.(iv) The mean, median, and mode are all equal.

Summary:

For the given observation X ; 7, 5, 6, 4, 7, 8, 12, the mean, median, and mode are all equal.