The mode of the given data 7, 9, 11, 13, 9 13, 9, 9, 7, 8 is
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Solution

Mode is that value of the observation which occurs most frequently i.e. an observation with maximum frequency is called mode. In the above set of observations, '9' occurs most frequently and so it is the mode of the given data.

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A survey was conducted to identify vegetarians in a group of people. Find the mode of the data.

Group	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$	$13 - 15$	$15 - 17$
Frequency	$6$	$7$	$3$	$7$	$12$	$9$

Q. The following table of grouped data represents the weight (in kg) of

100

gas cylinders. Calculate the mode weight of a cylinder.

Weight $(%)$	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$	$13 - 15$
Number of gas cylinders	$16$	$13$	$15$	$25$	$14$	$17$

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

Q. Evaluate:

(i) \frac{3}{7} + \frac{- 4}{9} - \frac{- 11}{7} - \frac{7}{9}

(i i) \frac{2}{3} + \frac{- 4}{5} - \frac{1}{3} - \frac{2}{5}

(i i i) \frac{4}{7} - \frac{- 8}{9} - \frac{- 13}{7} + \frac{17}{9}

“Did you understand?” Jack asked. At this, Jacob said, “I understood what mode is. Give me any question, I can find the mode of the observations.” Jack smiled at him and said- “Okay, I will give you a question and 3 hrs to solve it.” Jacob felt strange as for finding mode, 3 minutes would be enough, why was he given 3 hrs? Then Jack gave the problem:

What is the mode of the following set of observations?

$\begin{matrix} 9 & 13 & 5 & 9 & 6 & 9 & 9 & 17 & 13 & 11 & 12 & 13 & 19 13 & 0 & 9 & 13 & 21 & 7 & 13 & 7 & 17 & 9 & 0 & 7 & 11 \end{matrix}$

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The mode of the given data 7, 9, 11, 13, 9 13, 9, 9, 7, 8 is ___

Mode is that value of the observation which occurs most frequently i.e. an observation with maximum frequency is called mode. In the above set of observations, '9' occurs most frequently and so it is the mode of the given data.

The mode of the given data 7, 9, 11, 13, 9 13, 9, 9, 7, 8 is
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