MEDIAN and MODE for Ungrouped Data

MEDIAN and MODE for Ungrouped Data

Elizabeth Borres

At the end of the lesson, students will be able to:

1. Calculate the mean, median, and the mode for ungrouped data.

2. Apply the mean, median and the mode in real life.

Sample and Weighted Mean

(Prepare paper and pen, calculator)

Multiple Choice

It is the measure of central tendency used when one data is more important than the other data.

• mean

• median

• mode

• weighted mean

Multiple Choice

What is the mean of the data below?

1 , 5 , 10 , 11 , 20

• 10

• 19

• 9.4

• 9.1

Multiple Choice

Your grade in Statistics are 88, 91 and 90.

What should be your next grade to get an average of 90?

• 91

• 89

• 90

• 88

Multiple Choice

Terrance's homework grade was a 72, his project grade was an 80 and his exam grade was an 82. Homework is worth 10% of the final grade, the project was worth 50%, and the exam was worth 40%.

What was Terrance's final grade?

• 80

• 78

• 82

• 76

How to find the median and the mode for ungrouped data?

What is median?

• The midpoint of the values after all observation have been ordered from the smallest to the largest, or from largest to smallest.

• Before getting the median, arrange the numbers from lowest to highest or from highest to lowest.

Example 1: The following are the final grades of the six students in mathematics: 87, 62, 91, 58, and 85.

• Arrange the numbers from lowest to highest.

• Check if the number is even or odd.

Example 2: The following are the final grades of the six students in mathematics: 87, 62, 91, 58, 99 and 85.

• Arrange the numbers from lowest to highest.

• Check if the number is even or odd.

Poll

Do you have any questions(s)?

Multiple Choice

Find the median: 12, 15, 13, 18, 23, 5?

• 14

• 16

• 16.5

• 18

Multiple Choice

What do you call the middle number when a given data is arranged in increasing order?

• mean

• median

• mode

• range

Multiple Choice

What is the median of the data 5, 3,1 5, 2?

• 1

• 2

• 3

• 5

Multiple Choice

Find the median of the following set of data, 142, 149, 148, 149, 150?

• 142

• 148

• 149

• 150

Properties of the median

• The median is a unique value, that is, there is only one median for a set of data.

• It is not influence by extremely large value or small values.

• It can be computed for ratio level, interval. level, and ordinal level.

• 50% of the observations are greater than the median and 50% of the observations are less than the median.

What is MODE?

• The value of the observations that appears most frequently.

Properties of the MODE

• The mode can be found for all levels of data (nominal, ordinal, interval, and ratio)

• The mode is not affected by extremely high or low values.

• A set of data can have more than one mode. It it has two modes, then it is BIMODAL.

• A disadvantage is that a set of data may not have a mode because NO VALUE appears more than once.

Example 1:

• What is the mode:3, 2, 4, 5, 4.

Example 2:

• What is the mode: 3, 2, 2, 4, 5, 4.

Poll

Do you have any questions(s)?

Multiple Choice

A data set can have more than one mode

• True
• False

Multiple Choice

The scores awarded to 25 students for an assignment were as follows:

4 7 5 9 8 6 7 7 8 5 6 9 8 5 8 7 4 7 3 6 8 9 7 6 9

What is the mode?

• 6

• 7

• 8

• 9

Multiple Choice

What is the mode?

• # happening the most

• the average

• biggest - smallest

• the middle #

Multiple Choice

3, 4, 5, 5, 5, 6,7
The mode of these numbers is

• 5
• 10
• 4
• 1