standard deviation pdf notes

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