2 Outcomes and the Type I and Type II Errors; 9. It aids in the representation of complex data in a simple and understandable manner. Jul 2, 2024 · 102 Most Useful Excel Formulas with Examples Section A – IS FUNCTIONS 1. Use the 1-sample analysis to determine whether a population mean is different from a hypothesized value. by Anders Kallner. Nowadays, statistics are widely used in data Statistics is a branch of mathematics, which deals with all aspects of data. However, there are two important and basic ideas involved in statistics; they Statistics is a branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations. In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes. When there is no variability in a sample, all values are the same, and List MF20 . If we have an Statistics. It assesses the average squared difference between data values and the mean. =DAYS This is a handy formula to calculate the number of days between two dates (so there’s no worries about how many days are in each month of the range). UCL = c + 3! c LCL = c ! 3" c. Among them, the following 111 formulas are the most common and crucial for statistical uses. Here are some basic statistics formulas that cover a range of concepts: Mean Formula. MST-002 DESCRIPTIVE STATISTICS S. There are three common ways of describing the centre of a set of numbers. Statistics Formula Sheet and Tables 2020. Keep in mind that k is condition number, F is the F value found from your ANOVA calculation, and MSE is the From the formula, x= + z˙so a z score between 2 and 2 means you are in the interval ( 2˙; + 2˙) and hence by the Empirical Rule 95% of the students taking the exam have z scores between 2 and 2. Suppose, for example, we want to find the probability of getting 4 heads in 10 tosses. We can write the formula for the standard deviation as s = √⅀(𝑥𝑖 − 𝑥̅) 2 𝑛−1 where ⅀ means “the sum of” 𝑥𝑖 represents each value x in the date 𝑥̅ is the mean of the 𝑥𝑖 values . Cronbach’s alpha coefficient ( ): A coefficient of consistency that measures how well a set of variables or items measures. For Sep 19, 2016 · Process: Formulate the hypothesis. Since there is only one value repeating itself, it is a unimodal list. Descriptive statistics such as the mean, median and mode. The value of z* for a specific confidence level is found using a table in the back of a statistics textbook. Statistics for Social Scientists Quantitative social science research: 1 Find a substantive question 2 Construct theory and hypothesis 3 Design an empirical study and collect data 4 Use statistics to analyze data and test hypothesis 5 Report the results No study in the social sciences is perfect Use best available methods and data, but be aware In the above example, a confidence level of 95% was selected. You can apply these to assess only one variable at a time, in univariate Jan 27, 2023 · Basic Statistics Formulas: Download Concepts PDF. Inference – Methods for making predictions about a population (total set of subjects of Chart for number of defects/nonconformances per sampling unit – c Chart. mean then squared. , x 1 – a, x 2 – a, x 3 – a,. This resulted in a smaller standard deviation. g. Elsevier, 2013, ISBN 9780124 169715. Example =YEAR(7/16/2005) would return 2005. ) CL = c. The median is the middle number. Probability. Units must be in double quotes. Find the mean number of plants per house. There are 3 main types of descriptive statistics: The distribution concerns the frequency of each value. For example, if N represents the number of students in a statistics class, N would be a discrete variable. I. Solved Examples Example 1: function (pdf) f that satisfies f (x) O and f = 1, with P(a < < b) = f (x)dx. Consistency rating: 5 The explanations are consistent and build from and relate to corresponding sections that are listed in each unit. Class Median is the first class with the value of cumulative frequency equal at least n/2. Example: End Date October 12, 2015 minus Start Date March 31, 2015 = 195 days As an example: creating tables, sorting, and /or filtering data will not work properly if there are gaps in the data. Set Theory The old notion of: is (are) now called: Universal set Ω Sample space Elements of Ω(its individual ’points’) Simple events (complete outcomes) The definition of what is meant by statistics and statistical analysis has changed considerably over the last few decades. In this Statistics cheat sheet, you will find simplified complex statistical concepts, with clear explanations, practical examples, and essential formulas. Th eir comments and feedbacks were equally important and useful in making this book an excellent guide into the often-challenging fi elds of mathematics and statistics. The importance of this distinction will be discussed later. 1 Null and Alternative Hypotheses; 9. A survey was conducted by a group of students as a part of their environment awareness programmes, in which they collected the following data regarding the number of plants in 30 houses in a locality. Introduction. Guidelines for Data Structure 1 day ago · Probability and statistics are two key concepts in mathematics. For example: Where is the center of the data located? How spread out is the data? How correlated are the data from two variables? The most common descriptive statistics are in the following table, along with their formulas and a short description of what each one measures. statistics. Descriptive Statistics. Design - Planning/Implementing a study. It is based on literature [1, 6, 3] and in-class material from courses of the statistics department at the Univer-sity of California in Berkeley but also in uenced by other sou. 15. 👉🏻The updated probability of the subsequent, or conditional, event is multiplied by the probability of the preceding, or conditional, event to get conditional probability. ) 1. FORMULAS Related Links: Area And Perimeter Formula For All Shapes Pdf: Ab Formula: C To F Conversion Formula: Chemistry Formulas Pdf Download: Centigrade To Fahrenheit Formula: Heat Conduction Formula: Tangent Formula: X And Y Intercept Formula: Sample Mean Formula: Z Test Formula Use a Z test when you need to compare group means. 2. Function. √ : G−1 ;∗ ∗ 𝑆 ∗ @1 1 +1 2 A. Population mean = μ = ( Σ X i) / N; Population standard deviation = σ = sqrt [ Σ ( X i - μ ) 2 / N ] Mar 26, 2023 · This page titled 1. 1. Let X be a random variable with mean . Set the significance level. 1 Statistics is divided into two main areas, which are descriptive and inferential statistics. That is, P(Event) = (Number of ways event can occur) * P(One occurrence). In our research the focus in on descriptive statistics. While some view it as a standalone scientific field, others classify it as a separate branch within mathematics. Or use the 2-sample version to determine whether two population means differ. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. Step 2: Find the class mark by taking the midpoint of the upper and lower class limits. 3 days ago · Solved Examples for Class 10 Statistics. AVERAGEA. In other words, it is a mathematical discipline to collect, summarize data. 69. I hope and wish that the , A vs , vs , for example). 2 The Branches of Statistics 1. The mean, also known as the average, is a measure of central tendency in statistics. With the help of statistics, we are able to find various measures of central tendencies and the deviation of data values from the center. org6th March, 2011 This cheat sheet integrates a variety of topics in probability the-ory and. There are three essential characteristics of descriptive statistics we need to discuss: scales of measurement, measures of central tendency, and measures of v. The variability or dispersion concerns how spread out the values are. Feb 21, 2024 · It helps us collect, organize, analyze, and interpret data to find patterns, trends, and relationships in the world around us. Arrow down to binomial Pdf and press [ENTER]. Provides methods for. You can use inferential statistics to make estimates and test hypotheses about the whole population of 11th graders in the state based on your sample data. 1: Basic Definitions and Concepts is shared under a CC BY-NC-SA 3. FORMULAE 1 Measures of Central Tendency Mean for Ungrouped Data Mean for Grouped Data Weighted Mean Combined Mean n i i1 x X n ¦ In General n i i1 d XA n ¦ k ii i1 k i i1 fx X f ¦ ¦ k ii i1 k i i1 fd X A , f ¦ ¦ k i1 W k i i1 xw w ¦ ¦ 1 1 2 2 12 n X n X X nn k ii i1 k i i1 nX X n ¦ ¦ Median for distributions. It is denoted by f (x). Step 1: Construct the cumulative frequency distribution. Oct 23, 2020 · What is a normal distribution and how to use it in statistics? Learn the definition, formulas, examples, and applications of this common data pattern. Formulas and T erms. 1 The Five Basic Words of Statistics 1. Sep 20, 2023 · Better Education - Statistics discount textbook and endless questions package. ized by x-sub-i. Step 2: Decide the class that contain the median. For example, the sum of first n terms of a series in sigma notation can be represented as: ∑k=1n Xk ∑ k = 1 n X k. riability (or spread). Excel Function List We also have a large list of example formulas and video training. Oct 14, 2020 · Excel can be used to generate measures of location and variability for a variable. Variance is a measure of variability in statistics. INTRODUCTION TO STATISTICS Statistics is the branch of mathematics that deals with the techniques for collecting, analyzing, and drawing conclusions from data (Snedecor and Cochran, 1980). Aug 17, 2023 · For example, the variance formula uses "M" for mean, rather than x-bar. In-stead all parameters are treated as random variables with probability distributions. This function is positive or non-negative at any point of the graph, and the integral, more specifically the definite integral of PDF over the entire space is always equal to one. 3 Distribution Needed for Hypothesis Testing; 9. Enter the values for n, p and x into each cell. A Z test is a form of inferential statistics. The study of data collection, analysis, interpretation, presentation, and organisation is known as statistics. Here are two contrasting definitions of what statistics is, from eminent professors in the field, some 60+ years apart: "Statistics is the branch of scientific method which deals with the data obtained by counting or measuring 1. Introduction; 9. University, Atlanta, GA) The word STATISTICS FORMULASMEAN: The mean, symbolized by x-bar, equals one divided by the number of samples multiplied by the sum of all data points, sy. . Statistically Figuring Sample Size larizing statistics among the American public. You will soon understand that statistics and probability work together. is the symbol used to indicate that values are to be summed (see Sigma Notation) we. 5 Sample Selection Methods One-Minute Summary Test Yourself E very day, you encounter numerical information that describes or analyzes some aspect of the world you live in. In data analysis are primarily used two main statistical methods: descriptive statistics and inferential statistics. x n. Find the mode. Always remember one thing that it will only count the number. 3 Sources of Data 1. This chapter discusses these three statistics—mode, median, and mean—and demonstrates the advantages and draw-backs of each using a variety of examples. 2 Coefficient of variation It is sometimes useful to describe variability by Jun 28, 2024 · Mean, median, and mode are three important measures of central tendency in statistics. The mean add up all the numbers and divide by how many numbers there are. It is based on a more complete list of Excel functions here. =. 4 days ago · Add the terms to find the sum. For example, here are some news items Sep 4, 2020 · Example: Inferential statistics. Statistics are the analytical backbone of science. in@icir. Parameters. This includes: Types of data (categorical and numerical) Type of frequency distributions. After putting the value of z*, the population standard deviation, and the Stat 101 Formulas Brian Powers, Summer 2014 Sample Statistics Sample mean ̅= 1 Apr 19, 2020 · This reference book on applied statistics for hospitals was designed and developed to provide an elementary understanding of the terms, definitions, and formulae used in computing the hospital’s PREFACE AboutIntroductory Statistics IntroductoryStatisticsis designed for the one-semester, introduction to statistics course and is geared toward students Solved Examples on Statistics Formulas. Suppose we wish to find. Number of Plants. t of a study variable. Step 3: Tabulate the product of the class mark and its corresponding frequency for each class. Example 1: Age of students = {14,15,16,15,17,15,18}. The material supports students with Median and InterquartileRange – Grouped Data. 55 to 0. , x n – a. Jan 10, 2024 · The free cheat sheet covers key concepts and terminology for both descriptive and inferential statistics. 89; and low, 0. 70 to 0. This is the probability density function and will return you the probability of exactly x successes. If you leave off the x value and just enter n and p, you will get all the probabilities for each x from 0 to n. We begin by introducing two general types of statistics: •• Descriptive statistics: statistics that summarize observations. Also, we can say that statistics is a branch of applied mathematics. 1 What is Statistics? In common usage people think of statistics as numerical data—the unem-ployment rate last month, total government expenditure last year, the num-ber of impaired drivers charged during the recent holiday season, the crime-rates of cities, and so forth. Thus, there are 7 textbooks that have a discount out of 9 books. The central tendency concerns the averages of the values. What Are the Basic Statistics Formulas? The important statistics formulas are listed in the chart below: \(\begin{array}{|c|c|} statistics to get a feeling for the data. Scales of measurement are different ways to classify the measureme. 1. 3 days ago · Mean. Chart for number of defects/nonconformances per sampling unit - u Charts. Expectation is linear in that the expectation Of a linear combination Of functions is the same linear combination Of expectations. Statistics is a discipline of mathematics that deals with data analysis and numbers. Variables are frequently denoted with subscripts, for example, X where the subscript "i" takes on the Start Date – date furthest in the past. Jul 17, 2014 · Laboratory Statis tics, Handbook of. ? Bayesian: { There are no true model parameters. Mean (Arithmetic Mean) To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values. This formula is NOT in the function library. Step 1: Write your hypotheses and plan your research design. review ed by Dave K och and Emily Ryan (Emory. Test your knowledge with MCQs on various topics and access smart features like time to answer and smart answer key. Description – Graphical and numerical methods for summarizing the data. They are the mean, the median and the mode and are calculated as follows. ISBLANK =ISBLANK(value) If a cell is blank, it returns TRUE. Calculates the average of absolute deviations of its argument numbers from their mean. Expected values The expected value Of a function H (X) Of a random vari- able X is defined as = an. N/2 = 6/2 = 3 so average the 3rd and 4th values. Let us learn the basic statistics formulas along with a few solved examples. The COUNT function is used to count the number of cells containing a number. Also, Check: Previous Years IIT JEE Questions on Statistics for example). Statistics is a branch of science dealing with collecting, organizing, summarizing, analysing and making decisions from data. Step 2: Find the deviation of x i from a, i. These are typically processes where the outcome is influenced by many factors, each with small effect, but with significant total impact. obtain the following formula for the mean ( ̄x). Select the T ools Calculation of mean deviation for ungrouped data involves the following steps : Let us assume the observations x 1, x 2, x 3, …. Scribbr offers clear and concise explanations, diagrams, and calculators to help you master this topic. Complement of Event A: For mutually exclusive outcomes: Where not mutually exclusive For Independent outcomes: For dependent outcomes: P ( A _ and _ B ) P ( A )* P ( B A ) Discrete variables: =E(X) Normal Distribution. Here are some examples: Examples from Chemistry: What is thermal equilibrium? In statistics, we normally use words like “mean”, ”median” and “mode” to understand the data distributed throughout a range. In statistical mathematics, the mean value of a variable is described as the sum total of all the values of the variable divided by its number of values. To collect valid data for statistical analysis, you first need to specify your hypothesesand plan out your research design. It uses samples to draw conclusions about populations. (1) Mean or Average: Mean in theory is defined as the sum of all the elements of a set divided by the number of elements. 4) Definitional Formula: σ2= ∑ :X− Feb 27, 2023 · 1. Alpha scores are conventionally interpreted as follows: high, 0. Introduction to Statistics Basic Statistical Formulas Commonly used Ecological Equations. In simpler words, it is a field to collect and summarize data. From descriptive statistics we are considering mean, mode, median, quartiles, variance and ics describe the data. a single, unidimensional, latent construct in a scale or inven-tory. It is calculated by adding up all the values in a dataset and then dividing by the number of values. Make a conclusion. ) , X discrete. STANDARD The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics. This cheat sheet will make things easy when getting ready for Jun 10, 2015 · Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. N would also be discrete if it represented the number of r ooms in a house. Median. Since. The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics. example were much closer to the mean than those in the first example. Be it grouped or ungrouped, usually, these central tendency measures give a single data point which typically shows the behaviour of the whole data. Statistics Formulas Used on Stat Trek. { Random errors in data have no probability distribution, but rather the model param- 8 Events are subsets of the sample space (A,B,C,). 4. See WARNING below. 13. A Descriptive Statistics Suppose that a test in statistics course is given to a class at KSU and Cheat Sheet. Unit could be “Y” for years, “M” for months or “D” for days. 4) Computational Formula: σ= √ ∑X2− :∑X ;2 N R Basic Formula: σ= √SS R Computational Formula: s= √ ∑X2− ∑X ;2 n n − 1 Basic Formula: s= √SS n − 1 D) Variance (Ch. Modularity rating: 5 Modularity is a strength of this text in both the PDF and interactive online format. 96. 🤓The possibility of an event or outcome occurring based on the occurrence of a preceding event or outcome is known as conditional probability. The common formulas from the surface area and volumes chapter in 10 th class include the following: Here, l = length, b = breadth and h = height. The value of z* for a confidence level of 95% is 1. The data value with more repeats than any other data value. This web page lists statistics formulas used in the Stat Trek tutorials. If you are new to Excel formulas and how functions are used, see this introduction. Statistics is a study of data: describing properties of data (descriptive statistics) and drawing Direct Method to Find Mean. Jul 9, 2020 · Types of descriptive statistics. Since Excel recognizes adjacent rows and columns of data as a dataset, a blank row or column indicates the end of the data set, which can give partial views of the complete data set. Statistics- Set of methods for collecting/analyzing data (the art and science of learning from data). The formula in statistics: For almost all statistical computations, the basic concepts of mean, median, mode, variance, and standard deviation are the stepping stones. (b) If you scored 175 on the exam, what would your z-score be? From the formula, z= x ˙ = 175 150 10 = 2:5. Variance is one way to measure the amount a random variable \varies" from its mean over successive trials. Purpose. List of Formulae and Statistical Tables . VARIANCE: Variance, symbolized by s squared, equals 1 divided by the number of samples minus one, multiplied by the sum of each data point subtracted by th. 3 days ago · Basic Statistics Formulas. Introduction to Statistics, Data and Statistical Thinking 1. X continuous. You randomly select a sample of 11th graders in your state and collect data on their SAT scores and other characteristics. Formulas and Tables for AP Statistics. Inferential statistics such as t-tests, chi-square and correlation. Step 3: Find the median by using the following formula: ⎛ n ⎞ ⎜ - F ⎟. Decide the Test Statistic (z,t) Find out the critical value. 4 Sampling Concepts 1. Calculate this value for each pair. Here, k is the index of summation, 1 is the lower limit, and n is the upper limit. Learn the definitions, formulas, and solved examples of these concepts with Testbook, the leading online learning platform for competitive exams. Sep 13, 2023 · Basic Statistics Formulas. 4 Rare Events, the Sample, and the Decision and Conclusion Statistics and probability also play explicit roles in our understanding and modelling of diverse processes in the life sciences. Statistics, on the other hand, is involved with how we handle various data sets using various techniques. (x) and then divide the result by the number of values (n). An average is a measure of the centre of the data set. AVERAGE. Find out how to calculate the mean, standard deviation, and z-scores of a normal distribution, and how to compare it with other distributions. Vertex Form y= a(x h)2 + k or f(x) = a(x h)2 + k Test Statistics • Test Statistic for Population Proportion 𝑧𝑧= 𝑝𝑝 − 𝑝𝑝 0 𝑝𝑝0(1−𝑝𝑝0) 𝑛𝑛 • Test Statistic for population Mean t = 𝑥𝑥̅− 𝜇𝜇 0 𝑠𝑠 √𝑛𝑛 o with degrees of freedom = df=n-1 Aug 23, 2021 · Sample: Some data randomly chosen from population. , beginning date, ending date, etc. Business MBA students who studied business mathematics and statistics using the framework laid out in this book. Surface Area and Volumes Formulas For Class 10. Formula for COUNT function = COUNT(value1, [value2], …) Example of statistical function. To solve statistical problems, there are few formulas of statistics that will be used the most, they are as follows : Mean: To calculate the mean of a given data set, we use the following formula, Mean (\[\bar{x}\]) = \[\frac{\sum x}{N}\] Median: In the case of the median, we have two different formulas. Step 1: Classify the data into intervals and find the corresponding frequency of each class. Statistics in Maths: Statistics constitutes a mathematical discipline focused on gathering, scrutinizing, interpreting, and portraying data. Example: Assume a data set follows a normal distribution with a mean of 50 and a standard deviation of 10. Repeat this process for formulas that calculate a range of cells (e. The probability density function is defined as an integral of the density of the variable density over a given range. There are four categories we will consider Jun 16, 2024 · Excel has more than 450 functions for various purposes. Further Mathematics (9795) For use from 2017 in all papers for the above syllabuses. We introduced above the formula Var(X) = E[(X )2]. Computes the arithmetic average of its argument numbers. x. 90; medium, 0. Included in this chapter are the basic ideas and words of probability and statistics. Class 10 maths statistics mean am = a1 + a2 + a3 + a4 + a5/5 Σno/n. In statistical mathematics, the median of a data set of values is the centermost value of the data set when Definitional Formula: SS= ∑ :X− μ ;2 Computational Formula: SS= Q∑X2− :∑X ; 2 R E) Standard Deviation (Ch. If a cell is not blank, it returns FALSE. e. YEAR. Step 1: Calculate the central tendency measures to find the mean deviation and let it be ‘a’. Apr 14, 2021 · functions you should know, with links to detailed examples. descriptive statistics for a sample data: 2, 4, 6, and 8. Writing statistical hypotheses. For example: Where is Quadratic Functions and Formulas Examples of Quadratic Functions x y y= x2 parabolaopeningup x y y= x2 parabolaopeningdown Forms of Quadratic Functions Standard Form y= ax2 + bx+ c or f(x) = ax2 + bx+ c This graph is a parabola that opens up if a>0 or down if a<0 and has a vertex at b 2a;f b 2a . Data can be represented with a frequency table or with a bar graph. Understanding Formulas for Common Statistics - dummies After data has been collected, the first step in analyzing it is to crunch out some descriptive statistics to get a feeling for the data. =YEAR(Date) Returns the year portion of date. All data values have the same number of repeats. Here are some basic probability formulas: Probability of a single event: If an experiment has equally likely outcomes, the probability of a specific event E is given by: P(E) = number of favorable outcomes / total number of possible outcomes. The goal of research is often to investigate a relationship between variables within a population. Step 1. 📌Follow for more Learnbay #probability #conditionalprobability # First, we have to determine the probability of one possible way the event can occur, and then determine the number of different ways the event can occur. 18 hours ago · Notice that the formula for sample variance, `s^2`, is identical to the formula for population variance, except that we've swapped out `mu` for `bar x` (since `bar x` is sample mean, whereas `mu` is population mean), and we've changed N to n (since n refers to sample size, whereas N refers to population size). The variance of X, denoted Var(X), is de ned by Var(X) = E[(X )2]. (The subtlety here is that in c and u charts, a single unit may have more than one defect, while with p and np charts, an item is either defective or not. Cambridge Pre-U Mathematics (9794) and . . { Mathematical routines analyse the proba-bility of getting certain data, given a par-ticular model. 102 2x2 Augmented Matrix Examples 103 3x3 Augmented Matrix Example 104 Characteristic Equation and Eigenvalues 105 Eigenvectors 106 2x2 Eigenvalues and Eigenvectors – General Case 107 Calculating Inverses Using Characteristic Equations Chapter 15: Exponents and Logarithms 109 Exponent Formulas 110 Logarithm Formulas 111 e Jun 14, 2024 · Statistics in Maths. This notation asks to find the sum of Xk from k=1 to k=n. 1 Bar graphs and frequency tables. Unlike some other statistical measures of variability, it incorporates all data points in its calculations by contrasting each value to the mean. The distribution of cases across the attributes of any variable can be described using a variety of statistics. Average the middle 2 values. Each formula links to a web page that explains how to use the formula. • Step 2: Use this formula to find a set of Scheffe values you will use in the next step. Each bar represents a group of data and the bars can be compared to each other. AVEDEV. Definition 1. •• Inferential statistics: statistics used to interpret the meaning of descriptive statistics. We can get a fairly good idea about the whole set of Helpful tool for studying statistics formulas frequently used statistics formulas and tables chapter class width highest value lowest value (increase to next Oct 24, 2023 · The interquartile range or IQR is the difference between the third and first quartiles, which contains the middle 50% of the data. It’s best to use a table. No. Press [ENTER]. Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. Middle value in ordered data. Feb 8, 2024 · It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is based entirely on chance. 0 license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform. COUNT function. Formula (10) is same as σ = 1 N N 2 ( )2 f x f xi i i i− (11) (g) Another formula for standard deviation : σ x = N h ( ) N 2 2 f y f yi i− (12) where h is the width of class intervals and y i = xi A h − and A is the assumed mean. Example 2:In a class of 50, 4 students were selected at random and their total marks in the final assessments are recorded, which are: 812, 836, 982, 769. mj uv rn dg mw py rg sm fm st