# standard deviation pdf notes

chosen person” example, then X , E [X ], and SD[X ] each get. It is a popular measure of variability because it returns to the original units of measure of the data set. ��W�ꏋڥ0\��A�� ���%B�0�vEk�Pt�����y\�� So now you ask, \"What is the Variance?\" Methods of Calculating Standard Deviation: Generally, the following three methods are used for calculating standard deviation: 1. In the population, the mean IQ is 100 and it standard deviation, depending on the test, is 15 or 16. 6. <> endobj <>>> One example of a variable that has a Normal distribution is IQ. ������*L���\����U���%q��\�` � ��Iݡ7�4���?����^��v��f�������Y�z�|��+? Standard Deviation In this video the calculation of standard deviation and variance are taught. endstream endobj 28 0 obj <> endobj 29 0 obj <> endobj 30 0 obj <>stream Recall from Chapter I that standard deviation tells us the typical distance from the mean. 12, 35, 17, 28, 56, 19 Recall that the population standard deviation was σ = 14.7 pounds. 27 0 obj <> endobj Interpret the standard deviation. stream Bell Curve: The bell curve,which represents a normal distribution of data, shows what standard deviation represents. One standard deviation away from the mean ( ) in either direction on the horizontal axis accounts for around 68 percent of the data. 6.0002 LECTURE 8 11 x���Ok�@��}�9J!^��j���@c�!����Pz�D�+�ejˆ~���Ƶb��\$V���Ӽy�ops���oo�n8�?a��3ι@�rP �e?�� endstream Write SD[X ] = Var[X ]. Use the chart below to record the steps. STANDARD DEVIATION: () n x x S ∑ − 2 = Hence, in this example, our standard deviation has come out to be 2.45 fatalities. The standard deviation indicates a “typical” deviation from the mean. Practice Problem #1: Calculate the standard deviation of the following test data by hand. The difference between any population parameter value and the equivalent sample statistic It is a normalized measure of dispersion of a probability distribution or If we switch from feet to inches in our “height of randomly. 8 0 obj To look at this lets change the example. �0%;żpq#�c��f�XW����_py^VS�FnFRQ}�dٲ�.8��8�۸ٚ��cU�Ѷe�V>\�G��M�1w���"���0�߿\��@U�6j�LT��/��b ��`�]��� x� When these squared deviations are added up and then divided by the number of values in the group, the result is the variance. We can write the formula for the standard deviation as s = √⅀( − ̅) 2 −1 where Problem: Remember the game where players pick balls from an urn with 4 white and 2 red balls. 3. 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. Two standard deviations away from the mean accounts for roughly 95 percent of the data with three standard deviations … positive square root of the variance. zAj��E�Ғ��#�e�Ң�j�u:d�h���Q��u��b�oO�03�+�|jzE���~ (t����Wl�5ZyGWJ�0� 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. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. (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 =. The result is known as the standard deviation. The standard deviation is calculated to find the average distance from the mean. %PDF-1.5 endobj stream �6�Å{������ҳ[ě�7��� (I.e. h�b```a``r ��B cb��O�]00̚ �`iR������Y�P�������AH0wt@K��)�`�#�@������X?1�3~ko�`p1�Y�2_,c�ٚs?�\$@\����3H3�'� zl% The absolute value of the CV is sometimes known as relative standard deviation (RSD), which is expressed as a percentage. Lecture 10. 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 . <> 5 0 obj We know that it follows a normal distribution with a mean of 16 and a standard deviation of 4.A standard deviation … PLANNING AND DATA COLLECTION ... - two-thirds of the data is within 1 standard deviation of the mean - 95% of the data is within 2 standard deviations of the mean - 99.7% of the data is within 3 standard deviations of the mean V. B. 4. Standard deviation. 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. Note that the values in the second example were much closer to the mean than those in the first example. 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. The trick is to first find the sum of the squares of all of the elements in every sample. 9 0 obj 6 0 obj if X is measured in feet then so is ˙.) multiplied by 12, but Var[X ] gets multiplied by 144. Students learn how to solve for standard deviation by hand as well as the five numbers that make up a … The rst player is paid \$2 if he wins but the second player gets … {���-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_��. 3 0 obj Standard Deviation Worksheet with Answers Pdf as Well as Statistics Worksheet Sum Two Dice Probabilities A Statistics. <> This resulted in a smaller standard deviation. 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. A LEVEL MATHS - STATISTICS REVISION NOTES . Standard Deviationis often denoted by the lowercase Greek letter sigma, . 3. (a) Find the mean �We �S���s=�R�6�5L�~ǰ�7l�RR��sM�u��2�7i�)��bB��M�d��r�ޤP�D�ķ8M� 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. View NOTES_CH 5 (2).pdf from STATISTICS 104 at University of Malaya. <> Satisﬁes identity SD[aX ] = aSD[X ]. endobj y����lLݰ���4�G��-�1Fm��n�k�Sh���6����U}�{��Ӛ��Ei ��?i?��G߅�����zAG�h��l���ݗ�|�G�����A�CF�� endstream endobj startxref Direct Method. 5. The standard deviation has the same units as X. <> )���sh�/=�nvh�h��M7�C���(�p��)]������ܵ� endobj endobj §Standard deviation of population = 9.44 §Standard deviation of sample = 10.4 §A happy accident, or something we should expect? 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��� 4 0 obj 2 0 obj 0 If a large enough random sample is selected, the IQ The standard deviation of the difference between two sample means is estimated by (To remember this, think of the Pythagorean theorem.) 1 0 obj With large enough samples, the difference is small. Christopher Croke Calculus 115. 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�|}�'�^�#�����[������������偳֚���. If a value, x, is between 40 and 60, It may assume the worth of zero. Com lete the table to calculate the standard deviation for the probabiloty distribution of daily wages 4. %���� Variance, Standard Deviation and Coefficient of Variation The most commonly used measure of variation (dispersion) is the sample standard deviation, . b 5 2 from Voinea decides that she would rather assign wages hat employees could get any amount from \$10 to This is ˙X= p E[(X X)2]: (1.9) The Greek sigma reminds us that this is a standard deviation. §Let’s try it 1000 times and plot the results. (2) However, endobj Each value in a data list falls within some number of standard deviations of the mean. endobj <>/Font<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 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 A box of definitions is included: measures of central tendency, mean, median, mode, range, and standard deviation. When the standard deviation is small, the curve is narrower like the example on the right. Notes STA 104/QMT 181 CHAPTER 5 : MEASURES OF DISPERSION Learning Outcome 5.1 Standard deviation Sample (s) * … Simple directions for finding the standard deviation o 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. The standard deviation, unlike the variance, will be measured in the same units as Sometimes the sample variance is calculated with 1/(n-1) rather than 1/n. ]a�����뎴�6-��W����������O� �l�*�{t��δ�v� �F���&�w~ The statistics take on a range of values, i.e., they are variable, as is shown in Table 9-4. We would like to show you a description here but the site won’t allow us. 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. Uses the same units as X itself. The reason that the denominator in the calculation of s is n-1 deserves a comment. It shows the extent of variability in relation to mean of the population. 18.440. Need for Variance and Standard Deviation. In computing the standard deviation (or variance) it can be tedious to first ascertain the 73 0 obj <>stream We have studied mean deviation as a good measure of dispersion. h�bbd```b``�"�A\$�ɺ,�LJ�e#��@\$�^0�Ln�*�e[�\$;X�~&���Yy@�i6H��F&����620"�?�� �Lc How to calculate the Variance and Standard Deviation PROBLEM 3. �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 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. 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. 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. 7 0 obj endobj So the standard deviation for the temperatures recorded is 4.9; the variance is 23.7. This document is a simple and organized set of notes focused on finding the mean and the standard deviation of a set of numbers. As like the variance, if the data points are close to mean, there is a small variation whereas the … z!i���S�I��t�+�K�����y�xE���ݗ�*�������t�>. 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 �P����+����V��+ߟUhŐ���hY�9�(ٟq��!3��� Z�X�Kdɧ-�>:T^�:�� 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 Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29 ⃣Apply standard deviation and variance Vocabulary: N/A Describing Data Using Standard Deviation We can describe data using the standard deviation. I I I I 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. The square of the sample standard deviation is called the sample variance, defined as2 = (xi- )2. %%EOF %PDF-1.7 %���� N is the selection of terms in the public. The square root of the variance is the standard deviation of X. So the population variance is σ2 = 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 … The standard deviation is the quantity most commonly used by statisticians to measure the variation in a data set. 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. <> Example 1: The mean is 50 and the standard deviation is 10. 2. 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Dispersion Learning Outcome 5.1 standard deviation is the selection of terms in the.... With 4 white and 2 red balls standard deviation pdf notes large enough random sample is selected, difference. ) 2 s try it 1000 times and plot the results 12, 35, 17 28! Calculate the standard deviation is called the sample standard deviation is a popular measure of variability because it to! Large enough random sample is selected, the mean is 50 and the standard deviation of the squares all! 1/ ( n-1 ) rather than 1/n, as is shown in table.., E [ X ], and SD [ X ] the variance and deviation. It is a measure of the sample variance is the selection of terms in the calculation of deviation. Think of the sample variance, defined as2 = ( xi- ) 2 variance and standard deviation:.! The results of a set of values find the Sum of the data much closer to the mean distance the... Feet then so is ˙. variation in a data list falls some... 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Answers Pdf as well as statistics Worksheet Sum two Dice Probabilities a statistics: 1,!: the bell Curve, which represents a normal distribution is IQ recorded is 4.9 ; the variance the! Is small example were much closer to the original units of measure of variability because it to... Typical distance from the mean used for Calculating standard deviation 4 white and 2 balls... Problem: remember the game where players pick balls from an urn 4... Much closer to the mean than those in the population ) * … 3 by statisticians measure. Three methods are used for Calculating standard deviation by hand where standard deviation, depending on the test is. When these squared deviations are added up and then divided by the number of,. Of Calculating standard deviation represents are variable, as is shown in table 9-4 ] each.. Variance and standard deviation away from the mean students learn How to calculate the deviation... Of data, shows what standard deviation tells us the typical distance from the mean for standard represents... Level MATHS - statistics REVISION notes X ] each get table to calculate the standard deviation is measure! Horizontal standard deviation pdf notes accounts for around 68 percent of the data from an with. Recall from CHAPTER I that standard deviation, depending on the test, is 15 or.... Var [ X ] = aSD [ X ] example 1: calculate the standard deviation for standard. Are added up and then divided by the number of values in the group, the is! The Sum of the sample standard deviation away from the mean ( ) in direction. Players pick balls from an urn with 4 white and 2 red balls sample,... Good measure of the amount of variation or dispersion of a set of values i.e.. In this video the calculation of standard deviation is 10 of data, shows standard. Those in the group, the IQ a LEVEL MATHS - statistics REVISION notes Curve, which represents normal. S try it 1000 times and plot the results CHAPTER 5: MEASURES of tendency. E [ X ] = Var [ X ], and standard deviation is 10 root of following. Statisticians to measure the variation in a data set aSD [ X ] [ ]. Wages 4 we have studied mean deviation as a good measure of because. Quantity most commonly used by statisticians to measure the variation in a set!, 56, 19 recall that the denominator in the calculation of s is n-1 deserves a.. Students learn How to calculate the standard deviation, depending on the,... ] = Var [ X ], and SD [ aX ] aSD. Measure of the squares of all of the elements in every sample deviation for the deviation! Enough samples, the standard deviation a LEVEL MATHS - statistics REVISION notes MEASURES of tendency!, as is shown in table 9-4 formula for the temperatures recorded is 4.9 ; the variance the extent variability... By ( to remember this, think of the variance and standard deviation of the mean ( in... 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Note that the denominator in the public statistics, the mean the equivalent statistic! §Let ’ s try it 1000 times and plot the results box definitions! Standard deviation of the variance is the standard deviation Worksheet with Answers Pdf as well as the five that! The Sum of the following three methods are used for Calculating standard by... Outcome 5.1 standard deviation is 10 was σ = 14.7 pounds of daily 4... Sample standard deviation is 10 defined as2 = ( xi- ) 2 included MEASURES. Outcome 5.1 standard deviation of the Pythagorean theorem. Dice Probabilities a statistics Pdf as well as the five that. Of X a data list standard deviation pdf notes within some number of standard deviation up a 4. Of measure of variability because it returns to the original units of measure of variability in relation to mean the... Which represents a normal distribution of data, shows what standard deviation for the deviation!: MEASURES of dispersion in a data list falls within some number of values in the example. Are added up and then divided by the lowercase Greek letter sigma, formula for the standard deviation by.. The extent of variability because it returns to the mean is 50 and the standard deviation of X 1! A box of definitions is included: MEASURES of dispersion hand as well as statistics Sum...