Measures Of Central Tendency Of Ungrouped Data

MEASURES OF CENTRAL TENDENCY OF UNGROUPED DATA

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

1. Describe and illustrates the mean, median and mode. 2. Describe and interpret data using measures of central tendency.

IMPORTANCE OF CENTRAL TENDENCY a.To find representative value b.To make more concise data c.To make comparison d.Helpful in further statistical analysis

UNLOCKING OF USED TERMINOLOGIES 1. Central Tendency – is a summary statistic that represents the center point or typical value of a dataset. 2. Mean – it is used to describe a set of data. 3. Median – the middle value term in a set of data arranged according to size/medium (either increasing or decreasing). 4. Mode – is the measure or value which occur most frequently in a set of data. 5. Statistics – is a branch of mathematics that deals with the collection, classification, description and interpretation of data obtained by the conduct or surveys and experiments.

Mean Median Mode

Mean, Median and Mode are the three kinds of “averages”. There are many “averages” in statistics, but these three are the most common. In statistics, that single value is called the central tendency and Mean, Median and Mode are all ways to describe it.

WHAT IS MEAN? Mean is used to describe a set of data. To find Mean, add up the values in the data set and then divide by the number of values that you added. Example 1 Find the mean of the given numbers. 1,2,3,4,6,9,10,21

Solution 1,2,3,4,6,9,10,21 a. Add all the numbers 1+2+3+4+6+9+10+21 = 56 b. Divide 56 by 8 56 / 8 = 7

Therefore the Mean is 7

Example 2 Find the mean of these numbers 18, 21, 24, 36, 90 a.Add all numbers 18+21+24+36+90 = 189 b. Divide the answer by 5 189 / 5 = 37.8

Therefore the mean is 37.8

WHAT IS MEDIAN? Median is the middle value term of the data. Example 1 Find the median of 12, 3 and 5. 3, 5, 12 Therefore the median is 5

Example 2 Find the median of these numbers. 3, 13, 7, 5, 21, 23, 40, 23, 14, 12, 56, 23, 29 a. Put the numbers in order

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 29, 40, 56 Therefore 21 is the Median

Example 3. A marathon race was completed by 4 participants. What was the median race time? 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr Solution Ordering the data from least to greatest, we get:

2.7, 3.5, 5.1, 8.3 3.5 + 5.1 = 8.6

8.6 / 2 = 4.3

Therefore the median race time is 4.3 hr.

WHAT IS MODE? Mode is the measure or value which occur most frequently in a set of data. Example 1 Find the mode of these given numbers 6, 3, 9, 3, 3, 5, 9, 3 Arrange it in order

3, 3, 3, 3, 5, 6, 9, 9 Therefore the mode of these numbers is 3

GROUP ACTIVITY

Find the Mean, Median and Mode. Problem 1: (4, 8, 2, 8, 5, 9, 8, 2) Mean a. 4+8+2+8+5+9+8+2 = 46 b. 46 / 8 = 5.75 Median a. 2, 2, 4, 5, 8, 8, 8, 9 b. 5+8 = 13 c. 13 / 2 = 6.5 Mode a. 2, 2, 4, 5, 8, 8, 8, 9 b. Mode is 8

Find the Mean, Median and Mode. Problem 2: (13, 18, 13, 14, 13, 16, 14, 21, 13) Mean a. 13+18+13+14+13+16+14+21+13 = 135 b. 135 / 9 = 15 Median a. 13, 13, 13, 13, 14, 14, 16, 18, 21 b. The median is 14 Mode a. 13, 13, 13, 13, 14, 14, 16, 18, 21 b. Mode is 13

Find the Mean, Median and Mode. Problem 3: (11, 11, 8, 9, 10, 11, 12, 10, 13, 11) Mean a. 11+11+8+9+10+11+12+10+13+11=106 b. 106 / 10 = 10.6 Median a. 8, 9, 10, 10, 11, b. 11+11= 22

11, 11, 11, 12, 13

c. 22 / 2 = 11 Mode a. 8, 9, 10, 10, 11, 11, 11, 11, 12, 13 b. Mode is 11

VALUING Mean, Median and Mode are important in our everyday life. How? In Mean, or the average is important statistics used in sports. Coaches uses average to determine how well a player is performing. In Median, it is used in economics In Mode, may be beneficial for a manager to a shoe store.

ABSTRACTION 1. __________ it is used to describe a ______________. 2. __________ the _________________in a set of data arranged according to size/medium (either increasing or decreasing) 3. _______ is the measure or value which occur most ________ in a set of data. 4. ____________ is a branch of ____________ that deals with ____________, classification, description and ____________obtained by the conduct or surveys and experiments.

Assignment Write it in ½ crosswise paper Compute for the mean, median st and mode of your grades in your 1 nd and 2 grading period in any of your report cards.

THANK YOU!