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[image] 1990. [image]. POLYTECHNIC UNIVERSITY OF THE PHILIPPINES.

What is Data Management?. • Data Management is the process of collecting, storing, organizing, and maintaining data in a way that ensures accuracy, accessibility, and security. • It includes practices, tools, and systems for managing data effectively..

Importance of Data Management. • Supports decision-making through reliable insights. • Ensures data security and regulatory compliance. • Enhances efficiency and reduces redundancy. • Enables cost savings and fosters innovation..

Sets of numbers that have no common property. Steps in Data Management.

Real-Life Examples of Data Management. • Healthcare: Electronic health records improve patient care. • Retail: E-commerce platforms use data to personalize recommendations. • Banking: Tracks transactions and detects fraud. • Education: Manages student performance and records. • Logistics: Optimizes delivery routes and tracks shipments..

1. Basic Intersection Operations: Let A and B. Find A.

1. Complement of aset: Let U = be the universal set, and A = be a subset. Find N, the complement of with respect to U..

Show in excel.

1. Mean: The average value. 2. Median: The middle value when data is sorted. 3. Mode: The most frequently occurring value..

Find the (i) mean (ii) median (iii) mode for each of the following data sets : a) 12, 17, 20, 24, 25, 30, 40 b) 8, 8, 8, 10, 11, 11, 12, 12, 16, 20, 20, 24 c) 7.9, 8.5, 9.1, 9.2, 9.9, 10.0, 11.1, 11.2, 11.2, 12.6, 12.9.

(ii) Median Given data, 12, 17, 20, 24, 25, 30, 40 in ascending order. So, Median = middle value.

(8 + 8 + 8 + 10 + II + II + 12 + 12 + 16 + 20 + 20 + 24)/ 12 : (160)/12 Mean 13.33.

(7.9 + 8.5 + 9.1 + 9.2 + 9.9 + 10.0 + 11.1 + 11.2 + 11.2 + 12.6 + 12.9)/11 (113.6)/11 Mean - - 10.32.

For the data 11, 15, 17, x+1, 19, x–2, 3 if the mean is 14 , find the value of x. Also find the mode of the data..

Example: Is A a subset of B, where A = and B = 1 is in A, and 1 is in B as well. So far so good. 3 is in A and 3 is also in B. 4 is in A, and 4 is in B, That's all the elements of A, and every single one is in B, so we're done, Yes, A is a subset of B.

ACTIVITY From the given, apply set of language D UNION X D INTERSECTION X IS D a SUBSET OF X ?.

Example: A student's final grade is based on quizzes (30%), assignments (30%), and exams (40%). Their scores are: Quizzes: 80 Assignments: 90 Exams: 85 (80 x 0.3) + (90 x 0B) + (85 x 0.4) 24 27 34 Weighted Mean = -85.

Problem 2: Average Price of Goods A store sells three types of apples: Grade A apples: $3 per pound (weight: 5 pounds) Grade B apples: $2 per pound (weight: 10 pounds) Grade C apples: $1 per pound (weight: 15 pounds).

Solution: (3 5) + (2 10) + (l 15) weighted Mean 5+10+15 15+20+15 50 1.67 30 30 The weighted mean price per pound is $1.67..

QUIZ TIME.

Question 1 : The monthly salary (in P) of 10 employees in a factory are given below: 5000, 7000, 5000, 7000, 8000, 7000, 7000, 8000, 7000, 5000 Find the mean, median and mode..

Ron has a supermarket and he earns a profit of P5000 from his groceries, P2000 from vegetables and P 1000 from dairy products. He wants to predict his profit for the next month. He assigns weights of 6 to groceries, 5 to vegetables, and 8 to dairy products. Can you help Ron on how to calculate weighted average of his profits?.

Q. OOOL OOOL 0099 0008 0008 OOOL OOOL OOOL OOOL OOOL ooos ooos ooos epoL.•a ue!peu.l ueeb•a.

: 66000/10 : 6600 Mean • Median : : (7000 + 7000)/2 : 14000/2 : 7000 Mode 7000 is repeating 5 times. Hence mode is 7000. 6 x 5000 +9 2000 +8 x 1000 Weighted Average = 10000 30000 + 19 48,000/19 = 2,526.32 8000 Average Profit.

Various methods of representing sets, such as roster or tabular form, set- builder notation, and Venn diagrams..

DIFFERENCE OF PERCENTILE AND PERCENT. BASIS FOR PERCENTAGE COMPARISON Meaning What does it depict? Represents The percentage refers to the unit of measurement indicating, for every hundred. Scores out of hundred, or per hundred Rate, number or amount PERCENTILE Percentile implies a value, at or below which a specific proportion of the observations lies. Position or standing on the basis of appearance Rank.

“inter”-polation works within the scope of the given data..

FIND 37TH , 56th, 83th PERCENTILE?. Malh I aaO/0 of 50 qO/0 50.

A class of 50 students took a math test. John scored 75, and his score was higher than 43 students in the class. What is John's percentile rank?.

1. Statement form: In this, well-defined description of the elements of the set is given and the same are enclosed in curly brackets. For example: (i) The set of odd numbers less than 7 is written as:. (ii) A set of football players with ages between 22 years to 30 years. (iii) A set of numbers greater than 30 and smaller than 55,.

1). Find QI, Q2, and Q3 given the following scores using linear interpolation. 2, 10, 3, 8, 12, 15, 4, 9, 13.

Test scores: 55, 60, 65, 70, 75, 80, 85, 90, 95 (sorted) FIND: QI.

QUIZ TIME. SILENCE.

SILENCE.

Measures of Dispersion: Range, Standard Deviation, Variance.

Variability is crucial in statistics because it gives insight into the consistency (pagkakapareho) and reliability or truthfulness of data. Several ways to measure variability: Range – The difference between the highest and lowest values. Variance – Shows how much each value differs from the mean. Standard Deviation – A more interpretable measure that tells us the average distance of data points from the mean..

Range: Difference between max and min values. Range of [5, 10, 15] → Range = 15 - 5 = 10..

2 E(æt 2 (Population Variance) (Sample Variance).

EXAMPLE: TEST SCORES: 60,70,80,90,100. (Sample Variance) n—l.

A math problem with numbers Description automatically generated.

A teacher records the scores of five students on a math quiz: 80, 85, 90, 95, 100. What is the variance of the scores? Use population variance Solution: 1. Find the mean 2. Find each scores deviation from the mean then square 3. Find the variance 4. Explain answer.

1. 2. 3. Find the mean (average): = = = = Answer: The variance of the quiz scores is 50. This tells us how much the scores vary from the mean..

Problem 2: Variance in Daily Step Counts A person tracks the number of steps taken over five days: 6,000, 7,500, 9,000, 8,000, 7,000. Find the variance..

Problem 3: Comparing Variances of Two Classes Two classes take a test, and their scores are: Class A: 45, 50, 55, 50, 60 Class B: 40, 65, 55, 50, 45 Which class has a higher variance?.

I. Find the mean for each class: 2. +5=26 o o Class A Mean: = Class B Mean: {40 + 65 + 55 + 50 + = = 52 Calculate squared deviations for each ctass:l Class A: (45 - = 49 (50 - = 4 (55 (50 (60 - = 64 O Sum = 130 Variance = 130.

3. Standard Deviation: Average distance from the mean. SD is value from the square root of variance Average distance from the mean is 15.81.

Problem 1: Standard Deviation of Exam Scores A teacher records the exam scores of five students: 78, 82, 85, 90, 95. Find the standard deviation..

Find the mean (average): Mean =45} = 86 2. Find each score's deviation from the mean, then square it: = 16 3. 0 0 0 0 0 (82-"12 = (85-"12 = (90 - 9912 Find the variance: Variance =64+ 16+1 + Find the standard deviation (square root of variance): = Answer: The standard deviation of the exam scores is approximately 5.97. This means that, on average, the scores differ from the mean by about 5.97 points..

Problem 2: Standard Deviation of Daily Temperatures The recorded temperatures (°C) over five days were: 25, 27, 30, 32, 28. Find the standard deviation..

1. 2. 3. 4. 5. Find the mean: Mean = {25 27 +30 + 32 + = 28.4 Calculate squared deviations: 0 0 0 0 0 (25-4412 -1156 (27-?942- - (30 - 29412 (32 -2942 (28-?9412 = (-0.412 = 0•16 Find the variance: Variance= 11.56+1.96 2.56+12.96 = Find the standard deviation: {Standard Deviation) = Answer: The standard deviation of the temperatures is approximately 2.420C. This indicates the temperatures vary from the mean by an average of 2.420C..