# Measures of Central Tendency: Mean, Median and Mode

Views:

Category: Education

## Presentation Description

Get the measures of Central Tendency through Excel for Ungrouped and Grouped data

## Presentation Transcript

### PowerPoint Presentation:

Caught in the middle

### PowerPoint Presentation:

Are you really a Filipino? 115 ways to make sure ( Courtesy of the soc.culture.filipino newsgroup) … You point with your lips … You scratch your head when you don't know the answer. … You have a portrait of "The Last Supper" hanging in your dinging room wall …Your baon is usually something over rice

### PowerPoint Presentation:

How do we describe a set of data as a single number?

### PowerPoint Presentation:

Measures of Central Tendency We often need a single number to represent a set of data. This one number can be thought of as being “typical” of all the data. It intended to describe the center or middle of a set of data

### PowerPoint Presentation:

The Mean is the sum of the values divided by the number of observations (average) The Median is determined by sorting the data set from lowest to highest values and taking the data point in the middle of the sequence. The Mode is the most frequently occurring value in the data set.

### PowerPoint Presentation:

When do we use mean, median and mode?

### PowerPoint Presentation:

Measurement Scale Best measure of the “middle” Nominal Mode Ordinal Median Interval Symmetrical – Mean Skewed – Median Ratio Symmetrical – Mean Skewed – Median

### PowerPoint Presentation:

MEAN Use the mean to describe the middle of a set of data that does not have an outlier. Advantages Most popular measure in fields such as business, engineering and computer science. It is unique - there is only one answer. Useful when comparing sets of data . Disadvantage Affected by extreme values (outliers )

### PowerPoint Presentation:

MEDIAN Use the median to describe the middle of a set of data that does have an outlier. Advantages Extreme values (outliers) do not affect the median as strongly as they do the mean. Useful when comparing sets of data. It is unique - there is only one answer. Disadvantage Not as popular as mean.

### PowerPoint Presentation:

MODE Use the mode when the data is non-numeric or when asked to choose the most popular item. Advantages Extreme values (outliers) do not affect the mode . Disadvantages: Not as popular as mean and median. Not necessarily unique - may be more than one answer. When no values repeat in the data set, the mode is every value and is useless. When there is more than one mode, it is difficult to interpret and/or compare.

### PowerPoint Presentation:

How do we solve for the mean, median, and the mode?

### PowerPoint Presentation:

Ungrouped or Raw Data are those data which are not yet organized or arranged in a frequency distribution. Grouped Data are those data organized and summarized in the form of a frequency distribution. They have different ways to solve for the mean, median, and mode.

### PowerPoint Presentation:

Ungrouped Data = Mean Sum of all data Number of data

### PowerPoint Presentation:

Highlight the data. To compute for ∑x using Excel Then divide by n.

### PowerPoint Presentation:

Or you can get right away the Mean 83.3

### PowerPoint Presentation:

Highlight the data. Ungrouped Data Median Get the middle. 81.5

### PowerPoint Presentation:

Mode m ost common value bimodal 72 and 100

### PowerPoint Presentation:

Task #1 Measures of Central Tendency (Ungrouped) Save file as T2A1_surname

### PowerPoint Presentation:

How do we solve for the mean, median, and the mode for grouped data?

### PowerPoint Presentation:

Grouped Data = Mean Sum of (frequency * CM) This needs frequency distribution table

### PowerPoint Presentation:

=cell*cell (lower right corner) pointer changes drag to copy the formula of the 1 st cell Get the SUM

### PowerPoint Presentation:

Use the formula to solve for the mean. Mean = 85.6

### PowerPoint Presentation:

Additional Tips for making a Frequency Distribution Table: To identify the HV and LV of a data set: =min(data set) =max(data set) HIGHLIGHT the data set after typing the function

### PowerPoint Presentation:

Instead of using conditional formatting to count the frequency, you may use the formula =COUNTIF(data set,">= 70")- COUNTIF(data set,"> 74") Lower class limit Upper class limit

### PowerPoint Presentation:

Task #2 Measures of Central Tendency (Grouped) Save file as T2A2_surname

### PowerPoint Presentation:

Grouped Data m dn = Lcb me + Median lower class boundary of the median class c umulative frequency below the median class f requency of the median class class width

### PowerPoint Presentation:

Make a Cf < column. Locate the median class. C fb C fb = 21

### PowerPoint Presentation:

Find the L Cb of the median class L Cb = 84.5 fm = ? c = ? f me = 11 c = 5

### PowerPoint Presentation:

Organize the variables Solve for the median m dn = Lcb me +

m dn = Lcb me +

### PowerPoint Presentation:

Task #3 Measures of Central Tendency (Grouped) Save file as T2A3_surname

### PowerPoint Presentation:

Grouped Data mo = Lcb mo + ( ) c Mode lower class boundary of the modal class d ifference between the frequency of the modal class and the frequency before it d ifference between the frequency of the modal class and the frequency after it class width

### PowerPoint Presentation:

Find the L Cb of the modal class Modal class has the HIGHEST frequency

### PowerPoint Presentation:

Find the D 1 and D 2 D 1 D 2 D 1 = 11-5 = 6 D 2 = 11-9 = 2

### PowerPoint Presentation:

Organize the variables Solve for the mode mo = Lcb mo + ( ) c

### PowerPoint Presentation:

mo = Lcb mo + ( ) c

### PowerPoint Presentation:

Task #4 Measures of Central Tendency (Grouped) Save file as T2A4_surname

### PowerPoint Presentation:

How do the measures of central tendency affect the graphs?

### PowerPoint Presentation:

Negatively Skewed If the mean is less than the median and the median is less than the mode.

### PowerPoint Presentation:

Symmetrical Distribution If the mean, median, and the mode are equal.

### PowerPoint Presentation:

Positively Skewed If the mean is greater than the median and the median is greater than the mode.