If the mode of the following data is K, then the value of K in the data set 9, 8, 6, 7, 1, 6, 10, 6, 7, K² ? 12K + 42, 9, 7 and 13 i

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Solution

Q.
If the mode of the following data is K, then the value of K in the data set
9, 8, 6, 7, 1, 6, 10, 6, 7, K² − 12K + 42, 9, 7 and 13 is:

(i) 6 (ii) 9 (iii) 7 (iv) 13

Choose correct option from the following:

1 (iii) and (iv)

2 (i) and (iii)

3 Only (i)

4 (i) and (ii)

Ans.
(2)

In the above dataset, value 6 and 7 have occurred most number of times, i.e., 3 times.

Also, mode = K.

So, either 6 or 7 would be the mode.

If K = 6,
$K ² - 12 K + 42 = 6 ² - 12 (6) + 42 = 6$

If K = 7,
$K ² - 12 K + 42 = 7 ² - 12 (7) + 42 = 7$

∴ K = 6 and K = 7

So, (i) and (iii) are correct.

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