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=This Wiki is a online student source at Laichs for teaching the Concept of Central Tendency.=

=Definition of the Concept: YouTube Video=

__Students__ look at the following Video.

media type="youtube" key="df-BwzLp3Hc" height="315" width="420"


 * Grade/Subject: ** Los Angeles International Charter High School, Math 1, S-ID.A.2
 * Unit /Theme: ** Probability & Statistics

Statistics, Data Analysis, and Probability 1.1 Compute the range, mean, median, and mode of a data set.
 * Standards: **Mathematics Content Standards for CA Public __Schools__, High School

S-ID.A.2 __Students__ know the definitions of the range, mean, median and mode of a distribution of data and can compute each in particular situations.


 * __Students__: **

24 Students in Math 1


 * __Academic__ Language demands: **


 * 1) Students define the words mode, median, and mean from their prior understanding.
 * 2) Students discuss among themselves in groups the concepts of central tendency.
 * 3) Students discuss and draw/post visual representations of these central tendency trends.


 * Materials/Resources: **

Students use manipulatives which consist of plastic cups, markers, and plastic chips.

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Large white __paper__ is also needed for a bar graph and data presentation.


 * <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Development/Procedures: **

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Prior to the __application__ and implementation of this real-life lesson in Statistics and Probability, 24 students in the Math I class at Laichs were asked to __gather__ information about the number of sibling they may have in their individual households. Using this set of 24 numbers, students were asked to use the data set to discover its “trends” and the concept of central tendency. Initially, the __teacher__ seeks to __activate__ their prior knowledge of central tendency concepts by asking open-ended questions. . After clarifying any misunderstanding of these concepts, students are expected to discuss and share out definitions, computations, and differences in these three terms. Next students are asked to use their manipulatives which consist of cups, markers, and chips to construct visual representations of the same three terms of central tendency.

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Questions - Teacher-Student Collaboration


 * 1) <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Students are instructed individually to get their materials. Based on the numbers they were assigned from the data set, they will put the number of kissses corresponding to each number in each cup.
 * 2) <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">To discover mode, students are asked to place the labeled cups vertically in-line to create a bar graph based on all cups.
 * 3) <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">To discover the visual concept of median, students are asked to order each cup from least to greatest on their tables and find the cup/cups that represent the middle.
 * 4) <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">To discover the concept of mean or average, students are asked to attempt to put the same number of chips into each cup.

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;"> 5. Students create a Frequency Table and Draw a Histogram using the Data Set of 24 Numbers.... Challenge Problem !!!

**Group Work (Show your work)**
In a mathematics test, the marks of six students are 85, 22, 57, 58, 67 and 91.Find the mean of their marks

Find the median of the following set of data.

153, 137, 148, 149, 153

Find the mode of each of the following sets of data.

(a)

20, 21, 21, 24, 20, 27

(b)

1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Students will throughout the lesson be assessed informally and formally. The informal <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">assessments will be conducted through a series of questions by the teacher and via discussions <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">among themselves using Scribbler. The use and extent at which academic language is used will be assessed during these informal assessments by the instructor using Scribblar. Students will also be assessed formally through a quiz (see attached) at the conclusion of the lesson with defining, computing, and visually describing the individual terms of mode, median,
 * <span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">Assessment: **

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 24px;">Central Tendency Lesson- Exit Slip

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">The term **Central tendency** refers to how data looks toward the middle when you put it all in order. There are two central tendency numbers that can give us a “snapshot,” or summary, of a set of data. This single number can be more meaningful and easier to work with than a long list of number

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;">1. In your own words describe what the word mean means:

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;"> 2. In your own words describe what the word median means:

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;"> 3. In your own words describe what the word mode means:

<span style="font-family: &#39;times new roman&#39;,&#39;serif&#39;; font-size: 16px;">Using the set of data below from our lesson, find the **mode**, **median**, and **mean**.

<span style="font-family: &#39;times new roman&#39;,&#39;serif&#39;; font-size: 16px;">Also, //draw// or //describe// how your results can be represented visually.

<span style="font-family: &#39;times new roman&#39;,&#39;serif&#39;; font-size: 16px;">**82, 78, 73, 68, 95, 71, 58, 95, 71**

<span style="font-family: &#39;times new roman&#39;,&#39;serif&#39;; font-size: 16px;">1. What is the mean of the numbers above?

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;"> 2. What is the median of the numbers above?

<span style="font-family: &#39;Times New Roman&#39;,&#39;serif&#39;; font-size: 16px;"> 3. What is the mode of the numbers above?