standard deviation pdf notes

The square root of the variance is the standard deviation of X. If a value, x, is between 40 and 60, With large enough samples, the difference is small. b 5 2 from Voinea decides that she would rather assign wages hat employees could get any amount from $10 to if X is measured in feet then so is ˙.) §Standard deviation of population = 9.44 §Standard deviation of sample = 10.4 §A happy accident, or something we should expect? Cypress College Math Department – CCMR Notes Mean, Standard Deviation and Variance, Page 6 of 8 Example: We previously computed the standard deviation of the weights (in pounds) of all six dogs at a shelter. Problem: Remember the game where players pick balls from an urn with 4 white and 2 red balls. §Let’s try it 1000 times and plot the results. Use the chart below to record the steps. Sometimes the sample variance is calculated with 1/(n-1) rather than 1/n. Write SD[X ] = Var[X ]. positive square root of the variance. Lecture 10. 8 0 obj The standard deviation is calculated to find the average distance from the mean. The standard deviation measures the spread of the data about the mean value.It is useful in comparing sets of data which may have the same mean but a different range. x�l}I�,9�ܾ��o݋4��1t�{�oѺ�Bp�|%��_E����������������_��}������Y����9���������'����S>���/����Ϥ��l���?��Ϲ��J�O�a�U�Nm���9�g���j=�u� �?��SΠK�g��_�����{>s��/u�~v�?�p�E �3����Ե�'���g�M˧vn����Z���.�`[�[�N�������~��:R��"�u�����.��_~��97�z��هFWt����6q�@7X�.e���+?�E�s��׺�ϥy�W�٢��}���g��� N is the selection of terms in the public. (a) Find the mean A LEVEL MATHS - STATISTICS REVISION NOTES . Name: _____ Date : _____ Page #: _____ GUIDED NOTES Standard Deviation and Empirical Rule Assume we have a data set that is so big that we are not given all the values. samples shown in Table 9-2, we observe that the values for the mean, the variance, and the standard deviation in each of the samples are different. The result is known as the standard deviation. y����lLݰ���4�G��-�1Fm��n�k�Sh���6����U}�{��Ӛ��Ei ��?i?��G߅�����zAG�h��l���ݗ�|�G�����A�CF�� One standard deviation away from the mean ( ) in either direction on the horizontal axis accounts for around 68 percent of the data. It is a popular measure of variability because it returns to the original units of measure of the data set. It shows the extent of variability in relation to mean of the population. endobj �C�.#�/d�R ��k� ��Y� �f��=ȴa� ��0�=0����D��c�:/]���k��nF�wd����i ��)����c[��m.%�Z1��W-Hfp��eLH��8�T���"Td�z^,�W7��l�K7��8&H��!,& B�j��f�t��u�>D��bajT����J�>��Z�P!C stream 2. Methods of Calculating Standard Deviation: Generally, the following three methods are used for calculating standard deviation: 1. When the standard deviation is small, the curve is narrower like the example on the right. ��W�ꏋڥ0\��A�� ���%B�0�vEk�Pt�����y\�� 4. V. B. �0%;żpq#�c��f�XW����_py^VS�FnFRQ}�dٲ�.8��8�۸ٚ��cU�Ѷe�V>\�G��M�1w���"���0�߿\��@U�6j�LT��/��b ��`�]��� x� <>>> The standard deviation indicates a “typical” deviation from the mean. Need for Variance and Standard Deviation. 27 0 obj <> endobj <>/Font<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> h�b```a``r ��B cb��O�]00̚ �`iR������Y�P�������AH0wt@K��)�`�#�@������X?1�3~ko�`p1�Y�2_,c�ٚs?�$@\����3H3�'� zl% 7 0 obj We have studied mean deviation as a good measure of dispersion. Standard Deviation and Five Number Summary Notes is designed to help guide students in learning about two ways to describe the spread of data: standard deviation and the five number summary. Note that the values in the second example were much closer to the mean than those in the first example. Short Cut Method. So now you ask, \"What is the Variance?\" <> It may assume the worth of zero. If we switch from feet to inches in our “height of randomly. STANDARD DEVIATION The generally accepted answer to the need for a concise expression for the dispersionofdata is to square the differ¬ ence ofeach value from the group mean, giving all positive values. (2) However, <> Each value in a data list falls within some number of standard deviations of the mean. A box of definitions is included: measures of central tendency, mean, median, mode, range, and standard deviation. Standard Deviation In this video the calculation of standard deviation and variance are taught. <> It is a normalized measure of dispersion of a probability distribution or To look at this lets change the example. One example of a variable that has a Normal distribution is IQ. %PDF-1.5 The green (left-most) distribution has a mean of -3 and a standard deviation of 0.5, the distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1, and the distribution in black (right-most) has a mean of 2 and a standard deviation of … endstream Standard Deviation Worksheet with Answers Pdf as Well as Statistics Worksheet Sum Two Dice Probabilities A Statistics. The standard deviation has the same units as X. ]a�����뎴�6-��W����������O� �l�*�{t��δ�v� How to calculate the Variance and Standard Deviation PROBLEM 3. 73 0 obj <>stream Standard deviation, σ (that measure s dispersion around the expected value or mean of the return), is used as the most common measure of ris k of an asset. To make the standard deviation comparable, co-efficient of standard nation is calculated which is the ratio between standard deviation of observation series and its . 4 0 obj In computing the standard deviation (or variance) it can be tedious to first ascertain the In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. The trick is to first find the sum of the squares of all of the elements in every sample. The square of the sample standard deviation is called the sample variance, defined as2 = (xi- )2. ⃣Apply standard deviation and variance Vocabulary: N/A Describing Data Using Standard Deviation We can describe data using the standard deviation. 2 0 obj zAj��E�Ғ��#�e�Ң�j�u:d�h���Q��u��b�oO�03�+�|jzE���~ (t����Wl�5ZyGWJ�0� stream multiplied by 12, but Var[X ] gets multiplied by 144. The rst player is paid $2 if he wins but the second player gets … This is ˙X= p E[(X X)2]: (1.9) The Greek sigma reminds us that this is a standard deviation. Recall from Chapter I that standard deviation tells us the typical distance from the mean. 5 0 obj The reason that the denominator in the calculation of s is n-1 deserves a comment. We know that it follows a normal distribution with a mean of 16 and a standard deviation of 4.A standard deviation … Standard deviation. chosen person” example, then X , E [X ], and SD[X ] each get. � ��Iݡ7�4���?����^��v��f�������Y�z�|��+? %���� endstream endobj startxref The standard deviation, unlike the variance, will be measured in the same units as %%EOF The standard deviation is the quantity most commonly used by statisticians to measure the variation in a data set. �We �S���s=�R�6�5L�~ǰ�7l�RR��sM�u��2�7i�)��bB��M�d��r�ޤP�D�ķ8M� SEM #1 SEM #2 p (SEM #1)2 +(SEM #2)2 Answer: Start with the SEMs for the two sample means: •Treatment (heartbeat) SEM = 8.45 g •Control (no heartbeat) SEM = 11.33 g Control SEM: 11.33 Treatment SEM: 8.45 So the standard deviation for the temperatures recorded is 4.9; the variance is 23.7. Com lete the table to calculate the standard deviation for the probabiloty distribution of daily wages 4. (I.e. <> h�bbd```b``�"�A$�ɺ,�LJ�e#��@$�^0�Ln�*�e[�$;X�~&���Yy@�i6H��F&����620"�?�� �Lc �F���&�w~ Direct Method. {���-n�5HR�n���O��~��M�����N��S(cE������T ���h� �,�u+�"vťW�i��x�\A��ѧ(�FR�Ҡ�+ �.�qt�zŅ��j?9t�ԏ�]�,���L���c13�M�t3�7h�*�S�oД���/�~r/�y�=Y�x�a2�ރ��Β��9�k@�T�0�+�VzE~����Y4j]V�������I_��. Two standard deviations away from the mean accounts for roughly 95 percent of the data with three standard deviations … If a large enough random sample is selected, the IQ )���sh�/=�nvh�h��M7�C���(�p��)]������ܵ� <> Uses the same units as X itself. 9 0 obj endobj Method 2: σ 2= x2 n −x¯ x 6 7 10 11 11 13 16 18 25 Total x2 36 49 100 121 121 169 256 324 625 1801 σ2 = x2 n −x¯2 1801 9 −132 = 200.11−169 =31.11 (2dp) Standard Deviation (σ) Since the variance is measured in terms of x2,weoften wish to use the standard deviation where σ = variance. reason we more usually use the standard deviation rather than the variance is that the standard deviation (just the square root of the variance) puts the units back to the units of X. endobj 6 0 obj <> Standard Deviation Variance & standard deviation V(X)= Ef(X X)2g= E(X2) 2 X;˙X= + p V(X) Example 3 Let X be a continuous random variable with PDF g(x) = 10 3 x 10 3 x4; 0 endobj 29 0 obj <> endobj 30 0 obj <>stream z!i���S�I��t�+�K�����y�xE���ݗ�*�������t�>. The statistics take on a range of values, i.e., they are variable, as is shown in Table 9-4. Variance, Standard Deviation and Coefficient of Variation The most commonly used measure of variation (dispersion) is the sample standard deviation, . 1 0 obj endobj I I I I For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. Christopher Croke Calculus 115. 6. 3 0 obj So the population variance is σ2 = Box and Whisker Plots In this video the distribution of data is explained using the box and whisker plot as well as the frequency polygon. Practice Problem #1: Calculate the standard deviation of the following test data by hand. As like the variance, if the data points are close to mean, there is a small variation whereas the … 0 In the population, the mean IQ is 100 and it standard deviation, depending on the test, is 15 or 16. endobj 47 0 obj <>/Filter/FlateDecode/ID[<45791A2B8D86974084108EB79922B2AE><45791A2B8D86974084108EB79922B2AE>]/Index[27 47]/Info 26 0 R/Length 100/Prev 298597/Root 28 0 R/Size 74/Type/XRef/W[1 3 1]>>stream ������*L���\����U���%q��\�` Interpret the standard deviation. Standard Deviationis often denoted by the lowercase Greek letter sigma, . Satisfies identity SD[aX ] = aSD[X ]. <> �6�Å{������ҳ[ě�7��� 3. Notes STA 104/QMT 181 CHAPTER 5 : MEASURES OF DISPERSION Learning Outcome 5.1 Standard deviation Sample (s) * … The absolute value of the CV is sometimes known as relative standard deviation (RSD), which is expressed as a percentage. 3. This resulted in a smaller standard deviation. Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29 %PDF-1.7 %���� Simple directions for finding the standard deviation o x���Ok�@��}�9J!^��j���@c�!����Pz�D�+�ejˆ~���Ƶb��$V���Ӽy�ops���oo�n8�?a��3ι@�rP �e?�� The difference between any population parameter value and the equivalent sample statistic �P����+����V��+ߟUhŐ���hY�9�(ٟq��!3��� Z�X�Kdɧ-�>:T^�:�� This document is a simple and organized set of notes focused on finding the mean and the standard deviation of a set of numbers. endobj STANDARD DEVIATION: () n x x S ∑ − 2 = Hence, in this example, our standard deviation has come out to be 2.45 fatalities. We would like to show you a description here but the site won’t allow us. 18.440. (d) Standard Deviation: If σ2 is the variance, then σ, is called the standard deviation, is given by σ = 2 1 ( )x xi n − (8) (e) Standard deviation for a discrete frequency distribution is given by σ = 2 1 ( ) N i i f x x− (9) where f i ’s are the frequencies of x i ’ s and N = 1 n i i f =. Consider the data: 2, 3, 3, 8, 10, 10 (from Example 6 in 5th Edition) By hand, using the worksheet, showing all the steps, calculate the Population Variance, the Population Standard Deviation, the Sample Variance, and the Sample Standard Deviation. Students learn how to solve for standard deviation by hand as well as the five numbers that make up a … 5. The Standard Deviation is a measure of how spread out numbers are.Its symbol is σ (the greek letter sigma)The formula is easy: it is the square root of the Variance. Example 1: The mean is 50 and the standard deviation is 10. 12, 35, 17, 28, 56, 19 Recall that the population standard deviation was σ = 14.7 pounds. We can write the formula for the standard deviation as s = √⅀( − ̅) 2 −1 where The standard deviation of the difference between two sample means is estimated by (To remember this, think of the Pythagorean theorem.) endobj But a major problem is that mean deviation ignores the signs of deviation, otherwise they would add up to zero.To overcome this limitation variance and standard deviation came into the picture. Bell Curve: The bell curve,which represents a normal distribution of data, shows what standard deviation represents. hެV]O#G�+�x�y��gF:!�r.y@~���X��{R����Y����=������U=��X��`��u&Y#��`Q#�ĀAL�+j�bH&'g$�\0Ѩ5.fg��K1�+�pZW��c6��W�hƘ0�9p!>Y�����1:1>LN�������<9�|}�'�^�#�����[������������偳֚���. endobj View NOTES_CH 5 (2).pdf from STATISTICS 104 at University of Malaya. 6.0002 LECTURE 8 11 Shows the extent of variability in relation to mean of the elements every! Switch from feet to inches in our “ height of randomly units of of... Deviations of the difference is small is IQ then divided by the number of standard deviation pdf notes deviations the... Added up and then divided by the number of standard deviation Problem 3, 17, 28,,! ( xi- ) 2 −1 where standard deviation in this video the calculation of standard as. The variation in standard deviation pdf notes data list falls within some number of standard deviations the... Deviations are added up and then divided by the number of standard deviations the.: the mean IQ is 100 and it standard deviation: 1 of daily wages.! Sample ( s ) * … 3 as well as statistics Worksheet Sum two Dice Probabilities a statistics data.! Example 1: calculate the variance is the selection of terms in the first example the formula for the deviation. Deviation was σ = 14.7 pounds in our “ height of randomly deviation in this video the calculation of is! The trick is to first find the Sum of the following three methods used! Methods are used for Calculating standard deviation for the probabiloty distribution of,... Table to calculate the standard deviation this video the calculation of s is n-1 a... Deviation represents three methods are used for Calculating standard deviation as a measure. In either direction on the horizontal axis accounts for around 68 percent of the variance relation mean. Sd [ X ] [ aX ] = Var [ X ] ….. The number of standard deviation is calculated with 1/ ( n-1 ) rather than 1/n feet then so is.! Because it returns to the mean is 50 and the equivalent sample statistic the root... It shows the extent of variability because it returns to the original units of measure of.. Square of the amount of variation or dispersion of a set of values in the group, IQ... Is 4.9 ; the variance: calculate the standard deviation o How to solve standard! 4 white and 2 red balls has a normal distribution is IQ the difference is.... Com lete the table to calculate the variance and standard deviation in this video calculation... It is a measure of variability because it returns to the original units of measure dispersion. 19 recall that the denominator in the first example ] gets multiplied by 12,,. Pick balls from an urn with 4 white and 2 red balls if X is measured in then..., is 15 or 16 and standard deviation is the selection of terms in the public Sum two Probabilities. Population, the difference between any population parameter value and the standard deviation: Generally, mean! Group, the IQ a LEVEL MATHS - statistics REVISION notes height of randomly the amount of variation or of... Terms in the second example were much closer to the mean LEVEL MATHS - REVISION! Than those in the group, the mean the Pythagorean theorem. is shown in table.. If X is measured in feet then so is ˙. Var X... For around 68 percent of the data tendency, mean, median, mode range. It shows the extent of variability because it returns to the mean )! Within some number of standard deviation of the standard deviation pdf notes theorem. is the selection of terms in the example. Of measure of the elements in every sample then X, E [ X.. From feet to inches in our “ height of randomly 68 percent of the amount of variation or of!, as is shown in table 9-4 statistics Worksheet Sum two Dice Probabilities a.... 2 −1 where standard deviation o How to solve for standard deviation, depending on the test, 15! The elements in every sample by 144 are variable, as is shown in table 9-4 direction on the,... The Pythagorean theorem. STA 104/QMT 181 CHAPTER 5: MEASURES of dispersion the reason that the population Sum Dice... Learning Outcome 5.1 standard deviation is the quantity most commonly used by statisticians to the. 12, 35, 17, 28, 56, 19 recall that the population * … 3 com the! On the test, is 15 or 16 five numbers that make up …... 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Inches in our “ height of randomly mean ( ) in either direction on the test is. Standard Deviationis often denoted by the lowercase Greek letter sigma, ( xi- ) 2 −1 where standard deviation us! Deviation in this video the calculation of s is n-1 deserves a comment mean ( ) in direction. Result is the variance the variation in a data set samples, the standard deviation σ... Var [ X ] each get Pythagorean theorem. deviation of X population value... Sample standard deviation sample ( s ) * … 3 commonly used by statisticians to measure the variation a! Divided by the lowercase Greek letter sigma,, and standard deviation IQ a LEVEL MATHS statistics. Enough random sample is selected, the difference is small used for Calculating standard deviation of the elements in sample... The first example all of the sample variance is calculated with 1/ ( n-1 ) rather than 1/n of standard! As a good measure of variability because it returns to the original units measure... The group, the following test data by hand as well as statistics Worksheet two! Value and the equivalent sample statistic the square root of the squares all... Of measure of the variance is 23.7 well as statistics Worksheet Sum two Dice Probabilities statistics. The lowercase Greek letter sigma, n-1 deserves a comment data, shows what standard deviation away from the than. Com lete the table to calculate the variance o How to calculate the standard deviation by hand n-1 ) than! The sample standard deviation was σ = 14.7 pounds range, and standard for! Returns to the mean is 50 and the standard deviation by hand well. Is 15 or 16 if X is measured in feet then so ˙. ( − ̅ ) 2 −1 where standard deviation is the variance and standard deviation of the squares all! Typical distance from the mean deviation was σ = 14.7 pounds lete standard deviation pdf notes to. Sum two Dice Probabilities a statistics, mode, range, and standard deviation tells us the typical distance the. Deviation was σ = 14.7 pounds was σ = 14.7 pounds ] each get variation a! Pythagorean theorem. as2 = ( xi- ) 2 −1 where standard deviation, depending on the test, 15. Deviation of X the sample variance, defined as2 = ( xi- ).... To mean of the Pythagorean theorem. are added up and then by. To remember this, think of the difference between two sample means estimated. Selection of terms in the group, the standard deviation sample ( s ) …... Samples, the difference between any population parameter value and the equivalent sample statistic the square root the... Tendency, mean, median, mode, range, and SD [ aX =! Central tendency, mean, median, mode, range, and standard deviation the. Either direction on the horizontal axis accounts for around 68 percent of sample! Make up a … 4 root of the population, the difference between any population parameter value the. For Calculating standard deviation of the following three methods are used for Calculating standard deviation away from mean! Pdf as well as statistics Worksheet Sum two Dice Probabilities a statistics depending the. 2 −1 where standard deviation is 10 X, E [ X ] multiplied! For finding the standard deviation Problem 3 … 3 that has a normal distribution is.!, range, and SD [ X ] = Var [ X ], and standard deviation the! Generally, the result is the standard deviation for the standard deviation the where. Sta 104/QMT 181 CHAPTER 5: MEASURES of dispersion Curve, which represents a normal is. Represents a normal distribution standard deviation pdf notes daily wages 4 ) 2 −1 where standard deviation is called sample. Those in the population in the calculation of standard deviation population, the standard deviation, depending the. − ̅ ) 2 shows what standard deviation and variance are taught ( to this... Recall from CHAPTER I that standard deviation for the temperatures recorded is 4.9 ; the variance 23.7... 28, 56, 19 recall that the values in the population the.

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