Everyday Statistics and probability : Pictograms, histogram, bar chat etc Primary 4 Third Term Lesson Notes Mathematics Week 11

Subject : Mathematics

Class :Primary 4

Term :Third Term

Week :Week 11

Topic :

Everyday Statistics and probability : Pictograms, histogram, bar chat etc

Previous Lesson :

•  Distinguish between 2D shapes and 3D shapes Primary 4 Third Term Lesson Notes Mathematics Week 10

 

Content

Lesson one

Everyday Statistics and probability : Pictograms, histogram, bar chat etc

Good morning, class! Today, we’re going to dive into a fascinating topic in mathematics called “Everyday Statistics and Probability.” We’ll specifically focus on pictograms, histograms, and bar charts. These are wonderful tools that help us organize and understand data. So let’s get started!

Let’s begin with pictograms. A pictogram is a graph that uses pictures or symbols to represent data. It is a fun and visual way to display information. Pictograms are commonly used to represent data about things we can count, like the number of books read by students in a class or the favorite fruits of the students in our school.

Now, let’s move on to histograms. A histogram is a type of bar graph that displays data in intervals or ranges. It is useful when we want to show how data is distributed across different categories or groups. Histograms are great for understanding patterns and trends in data. For example, we can use a histogram to display the heights of students in our class, grouped into ranges like 120-130 cm, 131-140 cm, and so on.

Finally, we have bar charts. A bar chart is another type of graph that uses rectangular bars to represent data. It is commonly used to compare different categories or groups. Each bar in the chart represents a category, and the height of the bar shows the value or frequency of that category. For instance, we can create a bar chart to compare the number of pets owned by students in our class, with categories like dogs, cats, birds, and fish.

Now, let’s see how we can create these graphs step by step. First, we need to gather our data. For example, let’s say we want to create a pictogram showing the favorite ice cream flavors of the students in our class. We can survey everyone and record their choices.

Next, we decide on a symbol or picture to represent each piece of data. For our example, we can use ice cream cones to represent each student’s favorite flavor. The number of cones will correspond to the number of students who chose that flavor.

After that, we create a key or legend to explain the symbols we’re using. This helps others understand the graph. In our case, we’ll include a key that says, for example, “1 ice cream cone = 2 students.”

Now, we’re ready to construct our pictogram. We draw a grid with columns and rows, and each cell represents a certain number of students. We fill the cells with the appropriate number of ice cream cone symbols based on the data we collected.

For histograms and bar charts, we start by labeling the x-axis and y-axis. The x-axis represents the categories or intervals, while the y-axis represents the frequency or value. We draw rectangular bars that correspond to the frequency or value of each category, making sure the bars don’t touch each other.

Remember, it’s important to choose an appropriate scale for the axes so that the graph fits the data well and is easy to read.

I hope this introduction to pictograms, histograms, and bar charts has been helpful, and you’re excited to explore these graphs further. Remember, statistics and probability are all around us, and understanding them can help us make sense of the world. Now, it’s time for you to create your own graphs and explore the fascinating world of data representation!

[mediator_tech]

Evaluation :

1. A pictogram uses ________ or ________ to represent data.
a) numbers, lines
b) pictures, symbols
c) colors, shapes

2. A histogram is a type of ________ graph that displays data in intervals or ranges.
a) pie
b) line
c) bar

3. In a bar chart, each bar represents a ________ and the height of the bar shows the ________.
a) number, category
b) category, value
c) value, number

4. Pictograms are commonly used to represent data about things we can ________.
a) measure
b) count
c) observe

5. A histogram is useful for understanding patterns and ________ in data.
a) colors
b) trends
c) symbols

6. The x-axis of a graph represents the ________ and the y-axis represents the ________.
a) frequency, categories
b) categories, frequency
c) intervals, values

7. Pictograms help us visualize data in a ________ way.
a) visual
b) numerical
c) logical

8. A bar chart is used to compare different ________ or ________.
a) symbols, numbers
b) intervals, ranges
c) categories, groups

9. The rectangular bars in a histogram represent the ________ of each category.
a) width
b) frequency
c) shape

10. Choosing an appropriate ________ for the axes is important to create a readable graph.
a) scale
b) legend
c) color

Remember to choose the correct option (a, b, or c) that best completes each statement. Good luck!

 

Lesson Two

Worked examples on Everyday Statistics and probability : Pictograms, histogram, bar chat etc

Good morning, class! Today, we’re going to work on some examples to help us better understand the topic of Everyday Statistics and Probability, specifically pictograms, histograms, and bar charts. Let’s dive in!

Example 1: Let’s say we conducted a survey in our class to find out the favorite fruits of the students. The results are as follows:

• 8 students like apples
• 5 students like bananas
• 3 students like oranges
• 4 students like grapes

We can represent this data using a pictogram. Here’s how it would look:

Apples: 🍎🍎🍎🍎🍎🍎🍎🍎

Bananas: 🍌🍌🍌🍌🍌

Oranges: 🍊🍊🍊

Grapes: 🍇🍇🍇🍇

In this pictogram, each fruit symbol represents one student. By counting the symbols, we can easily see the number of students who like each fruit.

 

Example 2: Let’s create a histogram to represent the heights of the students in our class. Here are the heights (in centimeters) of 10 students:

120, 130, 125, 135, 132, 128, 130, 140, 133, 127

To create a histogram, we first need to decide on the intervals or ranges. Let’s choose intervals of 10 centimeters.

Interval: 120-129: ████

Interval: 130-139: ██████

Interval: 140-149: █

 

In this histogram, each bar represents the number of students within a specific height range. By counting the bars, we can determine how many students fall into each interval.

 

Example 3: Now, let’s work with a bar chart. We want to compare the number of pets owned by the students in our class. Here’s the data we collected:

• 6 students have dogs
• 4 students have cats
• 2 students have birds
• 3 students have fish

To create a bar chart, we’ll represent each category with a rectangular bar. The height of each bar will represent the number of students who have that type of pet.

 

[mediator_tech]

 

Bar Chart:

Dogs: ██████

Cats: ████

Birds: ██

Fish: ███

In this bar chart, we can clearly see the comparison between the different categories and the number of students who own each type of pet.

Remember, these are just a few examples to help you understand how to use pictograms, histograms, and bar charts. Practice using different data sets and create your own graphs to explore the world of statistics and probability. Keep up the great work, and soon you’ll become experts in representing and analyzing data!

[mediator_tech]

Evaluation

1. A pictogram is a graph that uses ________ or ________ to represent data. a) numbers, lines b) pictures, symbols c) colors, shapes
2. In a pictogram, each ________ represents a certain number of data. a) picture b) symbol c) color
3. A histogram is useful for displaying data in ________ or ________. a) ranges, intervals b) colors, shapes c) lines, patterns
4. The height of the bars in a histogram represents the ________ or ________ of the data. a) width, length b) frequency, value c) shape, size
5. Bar charts are commonly used to compare different ________ or ________. a) colors, shapes b) categories, groups c) patterns, trends
6. The x-axis of a graph represents the ________ and the y-axis represents the ________. a) intervals, values b) categories, frequency c) frequency, categories
7. Pictograms are a visual way to represent ________. a) numbers b) data c) trends
8. Histograms are useful for understanding the ________ and ________ of data. a) patterns, trends b) colors, shapes c) symbols, numbers
9. Bar charts use rectangular bars to represent data, where the height of each bar represents the ________. a) width b) frequency c) color
10. To create a readable graph, it is important to choose an appropriate ________ for the axes. a) scale b) legend c) title

[mediator_tech]

Lesson Three

Everyday Statistics and probability : Mean, Media, Mode, Range

Good morning, class! Today, we’re going to explore the exciting world of Everyday Statistics and Probability, focusing on some important measures: mean, median, mode, and range. These measures help us make sense of data and understand its central tendencies and spread. So let’s get started!

First, let’s understand what each measure means:

1. Mean: The mean is also known as the average. It is calculated by adding up all the numbers in a data set and then dividing the sum by the total number of values. The mean gives us an idea of the typical value in a set of data.

2. Median: The median is the middle value in a data set when the numbers are arranged in order from least to greatest (or vice versa). If there is an even number of values, the median is the average of the two middle values. The median is useful for finding the middle value that represents the center of the data.

3. Mode: The mode is the value that appears most frequently in a data set. In other words, it is the value that occurs with the highest frequency. The mode helps us identify the most common or popular value in a set of data.

4. Range: The range is the difference between the highest and lowest values in a data set. It gives us an idea of how spread out or varied the data is. The larger the range, the more spread out the values are; the smaller the range, the closer the values are to each other.

Now, let’s look at an example to understand these measures better:

Example:
Let’s say we have the following data set representing the number of hours students studied for a math test:

5, 3, 6, 4, 2, 5, 7

To find the mean, we add up all the values: 5 + 3 + 6 + 4 + 2 + 5 + 7 = 32. Then, we divide the sum by the total number of values, which is 7. So the mean is 32 ÷ 7 = 4.57 (rounded to two decimal places).

To find the median, we arrange the values in order: 2, 3, 4, 5, 5, 6, 7. Since there are 7 values, the middle value is the 4th value, which is 5. So the median is 5.

To find the mode, we look for the value that appears most frequently. In this case, the number 5 appears twice, while the other numbers appear only once. So the mode is 5.

To find the range, we subtract the lowest value from the highest value: 7 – 2 = 5. Therefore, the range is 5.

These measures help us understand different aspects of the data set. The mean tells us the average study time, the median represents the middle study time, the mode shows the most common study time, and the range indicates the spread of study times.

Remember, statistics and probability are powerful tools that help us analyze data and draw meaningful conclusions. Keep practicing and exploring different data sets to become confident in using these measures. Great job, class!

Evaluation

1. The mean is also known as the ________ of a set of numbers.
a) average
b) middle value
c) most common value

2. The median is the ________ value in a data set.
a) highest
b) lowest
c) middle

3. The mode represents the value that occurs ________ frequently in a data set.
a) least
b) most
c) randomly

4. The range is calculated by subtracting the ________ value from the ________ value.
a) highest, lowest
b) lowest, highest
c) middle, average

5. The mean is calculated by ________ all the values and then dividing by the ________.
a) adding, total number of values
b) multiplying, range
c) subtracting, median

6. The median is useful for finding the ________ value in a data set.
a) smallest
b) largest
c) middle

7. The mode helps us identify the ________ value in a data set.
a) average
b) most common
c) range

8. The range gives us an idea of how ________ or ________ the data is.
a) spread out, varied
b) average, normal
c) small, large

9. If a data set has two middle values, the median is the ________ of the two values.
a) sum
b) product
c) average

10. The mode represents the value with the ________ frequency in a data set.
a) highest
b) lowest
c) equal

Worked Examples

Example 1:
Let’s say we have a data set representing the ages of students in our class: 8, 9, 8, 10, 7, 9, 10, 8. We want to find the mean, median, mode, and range.

To find the mean, we add up all the values and divide by the total number of values. So, 8 + 9 + 8 + 10 + 7 + 9 + 10 + 8 = 69. Then, we divide 69 by 8 (since there are 8 values). The mean is 8.63 (rounded to two decimal places).

To find the median, we arrange the values in order from least to greatest: 7, 8, 8, 8, 9, 9, 10, 10. Since there are 8 values, the middle two values are 8 and 9. So, the median is (8 + 9) ÷ 2 = 8.5.

To find the mode, we look for the value that appears most frequently. In this case, the number 8 appears three times, which is more than any other number. So, the mode is 8.

To find the range, we subtract the lowest value from the highest value: 10 – 7 = 3. Therefore, the range is 3.

Example 2:
Let’s work on another example. Here’s a data set representing the number of siblings the students in our class have: 1, 0, 2, 1, 3, 1, 2, 1, 0.

To find the mean, we add up all the values and divide by the total number of values. So, 1 + 0 + 2 + 1 + 3 + 1 + 2 + 1 + 0 = 11. Then, we divide 11 by 9 (since there are 9 values). The mean is 1.22 (rounded to two decimal places).

To find the median, we arrange the values in order from least to greatest: 0, 0, 1, 1, 1, 1, 2, 2, 3. Since there are 9 values, the middle value is 1. So, the median is 1.

To find the mode, we look for the value that appears most frequently. In this case, the numbers 1 and 2 both appear three times, which is more than any other number. So, both 1 and 2 are modes.

To find the range, we subtract the lowest value from the highest value: 3 – 0 = 3. Therefore, the range is 3.

By using these measures, we can analyze and understand different aspects of the data sets. The mean gives us an average value, the median represents the middle value, the mode shows the most common value, and the range indicates the spread of values.

EVALUATION

1. The mean is also known as the ________ of a set of numbers.
a) average
b) middle
c) largest

2. The median is the ________ value in a data set.
a) highest
b) middle
c) smallest

3. The mode represents the value that occurs ________ frequently in a data set.
a) least
b) most
c) randomly

4. The range is calculated by subtracting the ________ value from the ________ value.
a) largest, smallest
b) smallest, largest
c) middle, average

5. The mean is calculated by ________ all the values and then dividing by the ________.
a) adding, total number of values
b) multiplying, range
c) subtracting, median

6. The median is useful for finding the ________ value in a data set.
a) smallest
b) largest
c) middle

7. The mode helps us identify the ________ value in a data set.
a) average
b) most common
c) range

8. The range gives us an idea of how ________ or ________ the data is.
a) spread out, varied
b) average, normal
c) small, large

9. If a data set has two middle values, the median is the ________ of the two values.
a) sum
b) product
c) average

10. The mode represents the value with the ________ frequency in a data set.
a) highest
b) lowest
c) equal

[mediator_tech]

Reference For Further Reading

1. Math is Fun (https://www.mathsisfun.com/): This website provides explanations, examples, and interactive activities for various mathematical topics, including statistics and probability.
2. National Council of Teachers of Mathematics (NCTM) Illuminations (https://illuminations.nctm.org/): NCTM Illuminations offers a wide range of lesson plans, activities, and games for teaching mathematics, including statistics and probability.
3. Khan Academy (https://www.khanacademy.org/): Khan Academy provides video lessons, practice exercises, and quizzes on various math topics, including statistics and probability.
4. BBC Bitesize – Maths (https://www.bbc.co.uk/bitesize/subjects/z826n39): BBC Bitesize offers interactive lessons, quizzes, and activities to help students understand and practice different mathematical concepts, including statistics and probability.
5. Math Playground (https://www.mathplayground.com/): Math Playground features math games, activities, and interactive tools that cover various mathematical topics, including statistics and probability
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