Statistics Module for Grade 7: Data Collection, Presentation, and Analysis, Study notes of Mathematics

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Module 19

STATISTICS

Have you ever wondered how a Covid-19 Vaccine's efficiency is determined by

medical scientists? Or why do people believe a meteorologist's weather forecast? Or

INTRODUCTION

• INTRODUCTION ---------------------------------------------------------------------------------------
  • Motivate
  • Explore
  • Discuss
• LESSON
  • Statistics ---------------------------------------------------------------------------------------------
• LESSON
  • Collection of Data ---------------------------------------------------------------------------------
• LESSON - Presentation of Data Using Frequency Distribution ----------------------------------
• LESSON - Graph -------------------------------------------------------------------------------------------------
• Innovate
• Assess
• References

perhaps you've wondered how scientists disproved the "earth is flat" theory. This is heavily reliant on Statistics! Did you know that statistics is utilized in a variety of fields by a variety of people? Scientists, mathematicians, economists, historians, political analysts, and even educators use it frequently. Because statistics can help people gain a better knowledge and correct information about a particular issue/problem/topic, develop a solution, draw a valid and reliable conclusion, and so on. This module will teach you how to define statistics, what data to collect and how to collect it, how to tabulate data in a frequency distribution, and how to use graphical representations. It will cover the following standards and competencies in particular;  Content Standards: The learner demonstrates understanding of key concepts, uses and importance of Statistics, data collection/gathering and the different forms of data representation, measures of central tendency, measures of variability, and probability.  Performance Standards: The learner is able to collect and organize data systematically and compute accurately measures of central tendency and variability and apply these appropriately in data analysis and interpretation in different fields.  Learning Competencies: Poses real-life problems that can be solved by Statistics (M7SP-IVa-2); Formulates simple statistical instruments (M7SP-IVa-3); Gathers statistical data (M7SP-IVb-1); Organizes data in a frequency distribution table (M7SP-IVc-1); and Uses appropriate graphs to represent organized data: pie chart, bar graph, line graph, histogram, and ogive (M7SP-IVd-e-1) As we begin in learning new and interesting lessons, it is important that you make sure that you are in the best condition to learn. Check on the following:  Are you in a conducive and suitable learning area?  Is your study area well-lit and free from unnecessary noise?  Do you have a prepared solution set, notebook and pen for your solutions and notes? If you are done, then, let’s start discovering new learning and acquire new skills!

MOTIVATE

This week's theme and sub-theme is "My Universe: Characteristics." Watch the video https://www.youtube.com/watch?v=HCDVN7DCzYE and answer the questions that follow.

1. What distinguishes the planet Earth from other planets?

▪ describe statistics; ▪ construct a real-life problems that can be solved using Statistics; and ▪ differentiate descriptive statistics from inferential statistics

DISCUSS

We can observe from the situation that Melissa went through a process to address or solve her problem (or question). We used to call what she did statistics! Hence, statistics refers to different of techniques and procedures for collecting , presenting , organizing , analyzing , and interpreting data. It's a tool for reacting intelligently to what you've heard, read, and experienced. Statistics may be useful in determining whether a test, program, or activity was successful or unsuccessful. Take studying for instance: either you will fail or you will pass. The methods (actions) you took may have determined the outcome. Example #1: You had a record of your Mathematics quiz scores, and you knew your strengths and limitations based on them. Let's examine what we can do with the statistical steps. Statistical Steps a. Collecting: Gathering all of your papers and making a note of your habits will reveal how well you did on those quizzes. b. Presentation: The amount of correct and incorrect answers you got, as well as your study habits, could be put into a table to show which items you find easy or difficult. c. Organization: Putting all of this data together will give you a clear view of your situation. Situation 1: Melissa, the class president, is curious as to who among her classmates would like a peer tutorial on the new Mathematics lesson. She began by asking each of them a question and recording their responses on the table. Then she realized that 18 of her classmates (out of a total of 25) wanted to participate in peer tutoring. Collecting Presentation Organization Analyzing Interpretation

Inferential Statistics is concerned in drawing a conclusion and make predictions given the information available. d. Analyzing : Examining the information offered in detail will reveal connections between your understanding of the topic and your study habits. e. Interpretation you can develop an explanation and come to a certain conclusion based on the data supplied, which is more likely and convincing. As you can see, this is a simple example, and you will encounter a more complex application of Statistics in the future as a result of these statistical stages. Do you already have a basic understanding of statistics? There are two types of statistics: descriptive and inferential statistics. Example #2: In a Grade 7 test scores, descriptive statistics may only describe the average test score. Meanwhile, inferential statistics may see the trends or may justify why the average test score is low or high. But why do we need to study statistics in the first place? Is it required to have prior understanding of the subject? The answer is a big YES! Statistics plays a big role in different sectors in our community and country. Statistics are important in many aspects of our community and country. Everywhere you look, statistics are being used, and you may have already been doing so! Take a look at the following statements:  Teenage Pregnancy is a factor in population growth.  The use of vaccines minimizes the number of cases of covid-19.  Because of the rise in suicide and depression, students are calling for an academic break.  Global warming is to blame for the change in weather.  A vaccine's effectiveness of 40% could leads to death  Eight out of ten Filipinos do not speak English.  In mathematics, men are smarter than women. Aren't they all real-life statistics examples? But do you know what's even more interesting? The fact that the above statements/claims may or may not be true; hence it necessitates verification and inquiry. Notice how these claims are different and random; some are from the fields of health, education, and economics, for example. This demonstrates how statistics can be applied to almost any aspect of modern life.

Your Turn

TRUE or FALSE Descriptive statistics is involved in summarizing and narrating data in an understandable and helpful way.

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 No. of hours (hrs) 3 3 1 2 2 1 2 Based from Situation 2 and Example #3, can you describe their data? What words would you use to explain the data in Situation 3? How about in Example #3? It is now time for you to learn about the two types of data: Categorical Data and Numerical Data. Categorical data includes dogs, cats, rabbits, fish, birds, and chicks. It's a type of information that can be categorized or ranked. While the data in Example #3 is a sort of data known as Numerical Data since it is presented in numerical form. Example #4: What kind of data would you get if you asked your classmates which subjects in Second Grade they got the lowest grade in? Because the possible categories include Araling Panlipunan, English, Filipino, MAPEH, Math, Science, Values, and so on, it is categorical data. Example #5: What type of data did you collect by recording the number of hours you spent studying each day over the period of a week? The data is a numerical data because the possible information you may get may look like this; Have you ever wondered how we gather data? What instrument are we going to use? We could employ a variety of statistical instruments to collect data. The tools or instruments used to collect data or describe a phenomenon are referred to as statistical instruments. The most common statistical instrument is the questionnaire under this are checklists, rating scales, and other tools. 10 What is your gender? o Female o Male oPrefer not to say oOthers What is your age? This is a sample of a Questionnaire. It is an instrument consists of standardized questions to gather information to one or more respondents. This could be done

Have you encountered or answered a questionnaire before? Maybe through Google forms? If yes, then maybe it looks like these. At the left side, that is what we called Checklist. It's a form of questionnaire that includes a list of things to check or complete. On the other hand, an example of a Rating Scales type of questionnaire may be found on the right side. It is a type of closed-ended answer in which an individual responds to a set of preset statements or questions. Have you paid attention to the questions posed to the three samples provided above? Did you notice any questions with predefined answers or options? What about questions that require a lengthy response or explanation? You can create a closed- ended or open-ended question while creating a questionnaire. o11 yrs. old Note: Questionnaire is different from survey. Survey is the act of gathering information using questionnaires. Yes No Do you know that there is no such thing as superior and inferior culture? Are you aware that there are different cultures around the world? Do you respect other cultures? Rate your feeling when someone tells you these: I hate you o Extremely sad o Little bit sad o Nothing at all I care for you o Extremely happy o Very happy o Happy o A little bit happy o Nothing at all

Situation 3: Teacher J is able to determine the number of students in Grade 7 Section 3 as well as the gender split. All he have to do is find the table written in the upper right corner of the whiteboard by the class secretary. This is how the table he saw looked. Sex Number Male 7 Female 8 Total 15

GOAL

At the end of the lesson, you will be able to: ▪ Describe frequency distribution ▪ Organize frequency distribution

DISCUSS

Situation 3 shows the purpose of tables. In statistics, the gathered data could be tabulated in a frequency distribution table. But first, let’s familiarize ourselves to the following terms; Frequency is the number of occurrence or observations the category appears. Frequency Distribution is a table that shows the categories and next to it are their frequencies In making a frequency distribution table, we have to consider what kind of table to use appropriate to our data. We have two types of frequency distribution; Ungrouped Frequency Distribution - is a table which data is not been organized in a group. It looks like a list of numbers or words. Example 10: Josh asks her classmates about the favourite colours. Here’s the raw (has not been processed) gathered data. blue black yellow violet green

violet black black, white blue green orange violet green black To construct an ungrouped frequency distribution, create a three column table. Colors (categories) Tally Frequenc y Black IIII 4 Blue II 2 Green III 3 Orange I 1 violet III 3 White I 1 Yellow I 1 Total 15 15 Grouped Frequency Distribution -is a table in which data has been organized into groups. It is usually used when the set of data range is large. Example #11 : Suppose the students from PNU conducted a survey to Grade 8 students about the number of minutes they could finish a 1-5 item word problems in Quadratic Equation. The following are the raw data gathered. 23 36 40 25 20 51 42 36 45 57 33 42 55 48 50 22 38 29 30 53 47 36 38 47 44 29 30 55 40 38 Class interval Tally Frequency Cumulative Frequency 50-57 IIIIII 6 24+6= 42-49 IIIIIII 7 17+7= 36-41 IIIIIIII 8 9+8= 28-35 IIIII 5 4+5= 20-27 IIII 4 4 Total 30 30 Write the colours or categories in the first column Tally the number of occurrence a category appears. Then count the total number of tallies in each category in numerical form.

Your Turn

Direction: Create a grouped frequency distribution with 5 classes using the data below. Kara conducted a survey within her community about the numbers of appliances a household owns. And here’s the raw data. 29 18 10 20 8 26 4 12 15 19 13 15 6 11 17 22 9 16 27 13

GOAL

At the end of the lesson, you will be able to: ▪ Differentiate the different graphs used in presenting the data ▪ Recognize the importance of using graphs.

DISCUSS

Have you ever watch news regarding covid 19? Then maybe you have see figures similar to these; LESSON 4 | Graphs

These figures are what we called Graph. It represents the data we gathered. It gives a clear image and easily to analyse. Here are the several graphs to use in presenting the data. Types of Graph Examples Pie graph or Pie Chart- a circular graph that is divided into sectors, and includes frequencies or percentage. Also, the quantity/percentage is proportional to the area it contains. The favourite subject of Grade 7-Camia is presented in a pie chart. 3% 13% 20% 23% 10% 13% 7% 10% Favorite Subjects of 7- Camia Mathematics English Filipino Science Araling Panlipunan MAPEH TLE Values Bar Graph or Bar Chart- is a way of presenting through plotting the data using a rectangular bars or columns that indicates the amount of observation of each category. There are two types of bar chart:

1. Vertical Column Graph -the height of the columns represent the frequency. 11 12 13 14 and above 0 5 10 15 Grade 7 Ages Grade 7 Ages
2. Horizontal Bar Graph - the length of the bars represents the frequency.

frequencies. 20-27 28-35 36-41 42-49 50- 0 10 20 30 40

No. of Minutes can Student Finish

the 1-5 Item Quiz in Mathematics

No. of Minutes

Your Turn

MATCHING TYPE:

Directions: Match the given situations in Set A to the appropriate graph to use in Set B.

INNOVATE

You wanted to know what are the cultures that a person familiar of. Then, create a PowerPoint presentation answering the following questions. You can be creative and includes some pictures/illustrations. Question 1: What type of data you will gather if you wanted to know the cultures that a person familiar of? Explain. Question 1: How would you gather the data? What type of statistical instrument you will use? Attach a sample here. Question 3: Since you’re able to identify what kind of data and instrument, how would you present it in a table? Is it grouped or ungrouped frequency distribution?

SET A SET B

1. The height of the sprout you planted within 6 days. a. Bar graph
2. Percentage of male and female in Grade 7-Camia b. Histogram
3. The test scores cumulative frequency. c. Line graph
4. Favourite book genre of your friends. d. Ogive
5. Grades in Mathematics of 10- Mabini. e. Pie chart

Class Interval Frequency Cumulative frequency 95-100 2 25 89-94 6 23 83-88 10 17 77-82 4 7 71-76 2 3 65-70 1 1 Question 4: What graph you will use in order to present the gathered data clearly? And why is it so?

ASSESS

Direction: Write the correct letter on your answer sheet.

1. What branch of Mathematics that is a process of collecting, presenting, organizing, analysing, and interpreting based on the given data? a. Statistics b. Differential c. Research d. Science of Experimenting
2. Which among the following examples describes inferential statistics? I. The total number of trash cans in Zone A. II. Planting trees help the environment to be cleaner. III. Philippine Region that has the hottest temperature. IV. One of the causes of air pollution is the air emitted by factories. a. I only b. II and III c. II and IV d. II, III, and I
3. Which kind of data is concerned with classification or rank of information? a. Categorical Data b. Numerical Data c. Quantified Data d. Ordered Data
4. Which among the following does NOT define a questionnaire? a. It is a type of survey. b. It can be in checklist or rating scale form. c. A statistical tool for gathering information. d. None of the above
5. What type of question does “Why do we need to plant trees?” under? a. Open question b. Close question c. Close-ended question d. Open-ended question
6. Categorical data uses what type of frequency distribution? a. Category table b. Grouped frequency distribution c. Classified frequency distribution d. Ungrouped frequency distribution Refer to the given table below 7-10 questions. Average Grades of 7-Rose in third quarter of Mathematics. 20