Question

2. Mode and median of the data 13,16,12,14,19,12,14,13,14 are
a) 13 & 14 b) 14&13
c) 14& 14 d) 19&13
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Answer 1

Answer :-

• The correct option is c)

To find :-

• The mode and median of the given data.

Step-by-step explanation :-

• Let's find the median and mode of the given data!

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Finding the median of the given data :-

• Here, the number of observations is 9, which is odd.

We know that :-

$\underline{ \boxed{\sf Median = \dfrac{n + 1}{2} \: th \: observation \: if \: n \: is \: odd}}$

Hence,

$\rm Median = \dfrac{9 + 1}{2} \: th \: observation$

$\rm Median = \dfrac{10}{2} \: th \: observation$

$\overline{ \boxed{ \rm Median = 5th \: observation}}$

Arranging the data in ascending order,

• 12, 12, 13, 13, 14, 14, 14, 16, 19.

Here,

• The 5th observation is 14.

Therefore,

• Median of the given data is 14.

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Finding the mode of the given data :-

• We know that, the number which occurs more times than any other number in the given data is it's mode.

Here, we observe that :-

• 14 occurs more times than any other number and it's frequency is 3.

Therefore,

• Mode of the given data is 14.

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$\overline{\underline{ \boxed{\bf Hence,\!\: option \: c \: is \: correct}}}$