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Learning Outcomes

Nội dung chính

    Learning Outcomes
    Mean, Median, and Mode
    Which measure of central tendency is obtained by calculating the sum of values and dividing this figure Brainly?
    What measure of central tendency is calculated by adding all the scores then dividing the sum of the number of scores?
    Which measure of central tendency equals the sum of the data values in a set divided by the number of data values apex?
    Which measure of central tendency is divided from the most common value?

Let’s begin by trying to find the most “typical” value of a data set.

Note that we just used the word “typical” although in many cases you might think of using the word “average.” We need to be careful with the word “average” as it means different things to different people in different

contexts.  One of the most common uses of the word “average” is what mathematicians and statisticians call the arithmetic mean, or just plain old mean for short.  “Arithmetic mean” sounds rather fancy, but you have likely calculated a mean many times without realizing it; the mean is what most people think of when they use the word “average.”

Mean

The mean of a set of data is the sum of the data values divided by the

number of values.

examples

Marci’s exam scores for her last math class were 79, 86, 82, and 94. What would the mean of these values would be?

The number of touchdown (TD) passes thrown by each of the 31 teams in the National Football League in the 2000 season are shown below.

37 33 33 32 29 28 28 23 22 22 22 21 21 21 20

20 19 19 18 18 18 18 16 15 14 14 14 12 12 9 6

What is the mean number of TD passes?

Both examples are described further

in the following video.

://.youtube/watch?v=3if9Le2sO0c

Try It

The price of a jar of peanut butter 5 stores was $3.29, $3.59, $3.79, $3.75, and $3.99. Find the mean price.

examples

The one hundred families in a particular neighborhood are asked

their annual household income, to the nearest $5 thousand dollars. The results are summarized in a frequency table below.

Income (thousands of dollars)
Frequency

15

6

20

8

25

11

30

17

35

19

40

20

45

12

50

7

What is the mean average income in this neighborhood?

Extending off the last example, suppose a new family moves into the neighborhood example that has a household income of $5 million ($5000 thousand).

What is the new mean of this neighborhood’s income?

Both situations are explained further in this video.

://.youtube/watch?v=1_4Hxcq8DpQ

While 83.1 thousand dollars ($83,069) is the correct mean household income, it no longer represents a “typical” value.

Imagine the data values on a see-saw or balance scale. The mean is the value that keeps the data in balance, like in the picture below.

If we graph our household data, the $5 million data value is so far out to the right that the mean has to adjust up to keep things in balance.

For this reason, when working with data that have outliers – values far outside the primary grouping – it is common to use a different measure of center, the median.

Median

The median of a set of data is the value in the middle when the data is in order.

example

Returning to the football touchdown data, we would start by listing the data in order. Luckily, it was already in decreasing order, so we can work with it without needing to reorder it first.

37 33 33 32 29 28 28 23 22 22 22 21 21 21 20

20 19 19 18 18 18 18 16 15 14 14 14 12 12 9 6

What is the median TD value?

Find the median of these quiz scores: 5

10 8 6 4 8 2 5 7 7

Learn more about these median examples in this video.

://.youtube/watch?v=WEdr_rSRObk

Try It

The price of a jar of peanut butter 5 stores was $3.29, $3.59, $3.79, $3.75, and $3.99. Find the median price.

Example

Let us

return now to our original household income data

Income (thousands of dollars)
Frequency

15

6

20

8

25

11

30

17

35

19

40

20

45

12

50

7

What is the mean of this neighborhood’s household income?

If we add in the new neighbor with a $5 million household income, then there will be 101 data values, and the 51st value will be the median. As we discovered in the last example, the 51st value is $35 thousand. Notice that the new neighbor did not affect the median in this case. The median is not swayed as much by outliers as the mean is.

View more about the median of this neighborhood’s

household incomes here.

://.youtube/watch?v=kqEu9EDkmfU

In addition to the mean and the median, there is one other common measurement of the “typical” value of a data set: the mode.

Mode

The mode is the element of the data set that

occurs most frequently.

The mode is fairly useless with data like weights or heights where there are a large number of possible values. The mode is most commonly used for categorical data, for which median and mean cannot be computed.

Example

In our vehicle color survey earlier in this section, we collected the data

ColorFrequencyBlue

3

Green

5

Red

4

White

3

Black

2

Grey

3

Which color is the mode?

Mode in this example is explained by the video here.

://.youtube/watch?v=pFpkWrib3Jk

It is possible for a data set to have more than one mode if several categories have the same frequency, or no modes if each every category occurs

only once.

Try It

Reviewers were asked to rate a product on a scale of 1 to 5. Find

The mean rating
The median rating
The mode rating

Rating
Frequency

1

4

2

8

3

7

4

3

5

1

Which measure of central tendency is obtained by calculating the sum of values and dividing this figure Brainly?

The mean, often called the average, of a numerical set of data, is simply the sum of the data values divided by the number of values.

What measure of central tendency is calculated by adding all the scores then dividing the sum of the number of scores?

The arithmetic mean is the most common measure of central tendency. It is computed by summing all the scores (sigma or Σ) and dividing by the number of scores (N):

Which measure of central tendency equals the sum of the data values in a set divided by the number of data values apex?

Mean. The mean of a set of data is the sum of the data values divided by the number of values.

Which measure of central tendency is divided from the most common value?

2 Mean. The most frequently used measure of central tendency is the mean. The mean, or more formally, the arithmetic mean, is simply the average of the group. That is, the mean is obtained by summing all the numbers for the subjects in the group and dividing by the number of subjects in the group.

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