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In this video, we will learn how to find and interpret the mode of a data set.
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The mode is an example of a measure of center or measure of central tendency.
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If we have a set of data, we can find a single number that represents the whole data set or give us some information about typical values by finding a measure of center.
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Examples of this are the mean, median, and mode.
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In this video, we will only discuss the mode.
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We will begin by looking at a definition.
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The mode of a data set is the value which appears most often.
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If two or more values appear most often, we can have more than one mode.
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Finally, if all of the values appear the same number of times, there is no mode in the data set.
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We will now look at some examples where we calculate the mode.
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The following data points represent the number of goals scored by a player in 10 consecutive matches: two, one, two, zero, one, two, one, four, four, and two.
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What was the mode score?
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We know that the mode of any data set is the value that appears the most often.
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In this question, we want to find the number of goals that were scored most often in the 10 matches.
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We could do this by inspection, just by looking at the data.
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However, it is often easier to do so using a frequency table or tally chart.
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In our frequency table, we have two rows: the number of goals and the frequency.
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As the least number of goals the player scored was zero and the highest was four, we have the integer values zero, one, two, three, and four.
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The player scored zero goals once in the 10 matches, as zero only appeared once in the list.
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They scored one goal three times, two goals four times.
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They didn’t score three goals at all, as there are no threes in the list.
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Finally, they scored four goals on two occasions.
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As there were 10 matches in total, our frequency row needs to add up to 10.
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One plus three is four.
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Adding four gives us eight, and adding two gives us 10.
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This is a quick check that insures we’ve used every item in the data set.
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As the mode is the value that appears most often, we need to find the value with the highest frequency.
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As four is the highest frequency and this corresponds to two goals, we can say that the mode score was two goals.
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The most common number of goals scored by the player in the 10 matches was two.
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We will now look at a question from a larger data set.
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The table shows the number of books that 30 students read in a year.
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Find the mode number of books read.
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We know that the mode of a data set is the value which appears the most often.
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In this question, we need to find the most common number of books read out of the 30 students.
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One way to do this is to set up a frequency table.
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Our frequency table in this question would have two rows: the number of books and the frequency.
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The least number of books read was one and the most was 10.
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Therefore, this row contains the integers from one to 10.
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There were two students that read one book in the year.
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Two students also read two books.
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There were three students that read three books.
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Four students read four books.
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Two of the students read five books.
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There were three students that read six books.
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Three students read seven books.
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Eight read eight books, two read nine books, and one student read 10 books.
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As there were 30 students in total, we need to check that our frequencies sum to 30.
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This is a quick check that ensures we have used each item from the data set.
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As the mode is the number that appears most often, we are looking for the highest frequency; this is eight.
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The frequency of eight corresponds to eight books.
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Therefore, the mode number of books read by the 30 students is eight.
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It is important in this question that our answer is given in terms of books read.
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Our next question involves finding the mode of nonnumerical data.
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A bookstore sold 11 books by Haruki Murakami, two books by Henry Thoreau, and six books by Carl Jung.
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Determine the mode for this data.
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We know that the mode of any data set is the value or item that appears most often.
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In this question, we have 11 books by Haruki Murakami.
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We have two books by Henry Thoreau.
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And finally, we have six books by Carl Jung.
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We are looking for the book that appears the most.
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As 11 is greater than two and six, 11 is the highest frequency.
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As this value corresponds to the books of Haruki Murakami, we can say that he is the mode for this data.
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The mode will be the author with the highest number of books.
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As mentioned at the start of this video, some data sets have more than one mode.
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This is one such question.
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Find the mode of the values four, seven, two, eight, nine, three, four, two, four, eight, six, and eight.
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The mode of a data set is the value that appears most often.
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We note however that there can be more than one mode if more than one value appears most often.
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We can begin this question by setting up a frequency table containing the value and the frequency.
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The lowest value from our list was two, and the highest value was nine.
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We will, therefore, include the integer values from two to nine.
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The number two appeared twice in the list.
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Therefore, it has a frequency of two.
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There was one three in the list.
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The number four appeared three times.
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There were no fives in the list.
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So, the frequency of five is zero.
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There was one six in the list.
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The number seven also appeared once.
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The number eight was in the list three times.
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And finally, there was one nine in our list of values.
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As there were 12 values altogether, we need to ensure that our frequencies sum to 12.
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As the frequencies two, one, three, zero, one, one, three, and one do indeed sum to 12, this is a quick check to ensure we have used each of the values from our list.
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As the mode is the value that appears most often, we are looking for the highest frequency.
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In this case, this is equal to three and corresponds to the values four and eight.
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As both four and eight appear three times in the list, the mode of this data set is four and eight.
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In this question, we have a situation where there is more than one mode.
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Our final question involves calculating the missing value in a data set when the mode is given.
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Elizabeth has the following data: three, six, four, five, and 𝑚.
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If the mode is six, find the value of 𝑚.
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We know that the mode of any set of data is the value that appears most often.
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In this set of data, Elizabeth has the numbers three, six, four, five, and the missing number 𝑚.
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We are also told that the mode is six.
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This means that the most popular, or most common, number is six.
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As three, four, five, and six all appear once at present, the only way that the mode can be six is if the missing number 𝑚 is six.
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The set of data three, six, four, five, and six will have a mode of six.
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It is usually very straightforward to find a missing number in a data set when given the mode.
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We will finish this video by summarizing the key points.
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The mode is an example of measure of center, otherwise known as a measure of central tendency.
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The mode of a set of data is the value which appears the most.
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In any specific data set, there could be one mode, more than one mode, or no mode at all.
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The set of data four, seven, six, seven, and five has one mode.
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This is equal to seven as seven occurs most frequently.
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The set of data five, eight, four, eight, and four has more than one mode.
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In fact, there are two modes: four and eight, as these occur more frequently than any other numbers.
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Finally, the set of numbers five, seven, six, two, and nine has no mode.
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This is because each of the numbers occurs just once.
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None of them occur more frequently than any other number.
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If we are given a large set of data, it is often useful to draw a frequency table or tally chart to display the data first.