“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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Both 9 and 13

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Solution

The correct option is B
Both 9 and 13

If we make an observation table for the data given in the question, we can get it as:

Here, 6 is the highest frequency and both 9 and 13 have the same frequency, i.e. 6. So, 9 and 13 both are the modes of this data set.

Note- A data set with 2 modes is called bimodal data set.

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Similar questions

“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?

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

The storekeeper was very happy to get a solution to his problem. When Jack told this story to Jacob, he was so curious to know how Jack solved the problem of the storekeeper. Then Jack explained the concept of mode to Jacob.

Mode of a data set is-

“You are William Playfair!!!” Jack exclaimed with super surprise. “Yes, I am”, he replied. While Jack was still in the state of astonishment, William asked him, “Can you help me again? I have a list of number of people who have attended the Mass and lunch offered at the church for four months. Can you help me compare this data?” According to his list, then, Jack drew a bar chart (which William doesn’t know anything about). It came as:

Looking at this, William exclaimed - “What a nice chart! We can easily compare the number of people. Thanks” Then Jack smiled and said- “If it’s that easy, tell me in which month the number of people attending Mass is maximum and in which month the number of people attending lunch is minimum?” The correct answer is –

Building something that wasn’t even discovered then would be surely a time taking job. That hardware store owner agreed to lend Jack a decent room at the roof of his house in return of teaching his son Jacob mathematics.

Next evening, Jack started the topic- “Methods to find central tendency.” He taught Jacob arithmetic mean. When the tuition was over, Jacob said- “I think arithmetic mean is the only method to measure the central tendency of a set of observations.” Say true or false.

“You are William Playfair!!!” Jack exclaimed with super surprise. “Yes, I am”, he replied. While Jack was still in the state of astonishment, William asked him, “Can you help me again? I have a list of the number of people who have attended the mass prayers and lunch offered at the church. But I am facing difficulty comparing them. Can you help me to compare them easily?” According to his list, then, Jack drew a bar chart (which William doesn’t know anything about). It came as:

Looking at this, William exclaimed - “What a nice chart! We can easily compare no. of people. Thanks” Then Jack smiled and said- “If it’s that easy, tell me in which month no. of people attending the mass prayers is maximum and in which month no. of people attending lunch is minimum?” The correct answer is –

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