Example find the sample mean and the range 1 3 3 3 3 3 2 1 2 3 4 5 3 1 1 3 5 7

Example find the sample mean and the range 1 3 3 3 3

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Example : find the sample mean and the range 1. 3, 3, 3, 3, 3. 2. 1, 2, 3, 4, 5. 3. -1, 1, 3, 5, 7. --------------------------------------------------------------------------------------- Variance Population variance Sample variance Standard deviation for the population for the sample Ms. Lubna Ineirat 55 Note:
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Population variance : Let x , x ,….x. be a population of size N, with mean μ , then the population variance is given by Example : evaluate 1, 2, 3, 4, 5. Example : evaluate -1, 1, 3, 5, 7. Ms. Lubna Ineirat 56
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Sample variance Let x , x ,….x. be a population of size n, with mean x , then the sample variance is given by Example : evaluate 10, 12, 11, 13, 15 ------------------------------------- Another formula for Ms. Lubna Ineirat 57
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Variance for frequency table Example : find Ms. Lubna Ineirat 58 Age Frequency 18 2 19 6 20 9 21 4 22 3 23 1 Total
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Example : find the variance and Standard deviation Ms. Lubna Ineirat 59 grades Frequenc y 1 - 5 6 6 - 10 9 11 - 15 12 16 - 20 3 Total
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Other descriptive measures Coefficient of variation is used to compare the variability of two data sets or more. Coefficient of variation C.V= Example: which sample has more variability? Ms. Lubna Ineirat 60 Sample 1 sample 2 age 10 years 25 years Mean weight 35 kg 75 kg variance 200 kg 200kg
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K th percentiles P : is the value where k% of data less than it Example: Given the following data 46 ,57,59 ,61 ,62 ,70 ,73 ,77,80 ,81 ,82 ,82 ,84 ,86 ,90 ,91 ,93, 95, 96. a. find the 20 th percentiles b. find the P c. Find P d. Find P e. Find P f. Find P Ms. Lubna Ineirat 61 To find P 1. Order the data from smallest to largest . 2. Determine the position of the percentile L=
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Percentiles and Quartiles Quartiles divide the data into 4 equal parts. o P : First quartile(Q ) means that 25% of the data less than or equal to Q or 75% of the data more than or equal to Q o P : Second quartile (Q ) = median means that 50% of the data less than or equal to Q Or 50% of the data more than or equal to Q o P : Third quartile (Q ) means that 75% of the data less than or equal to Q Or 25% of the data more than or equal to Q Inter quartile range (IQR)= Q - Q Is used to measure the variability when the data set is significantly sewed . Ms. Lubna Ineirat 62
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Box- and whisker plot To construct the Box plot we need the following values max /min /Q /Q /Q . Example : construct the box and- whisker plot for the following data. 7, 3, 14, 9, 7, 8, 12 Ms. Lubna Ineirat 63
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Example : construct the box and- whisker plot for the following data. 19, 21, 47, 55, 78, 65, 56, 6 15, 24, 38. Order the date from smallest to largest………………………………. Min=…………. Max=……………. P = Q P = Q P =Q Box- Plot Ms. Lubna Ineirat 64
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Skewed Data Data can be “ skewed” meaning it tends to have along tail on one side than the other . Ms. Lubna Ineirat 65
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The normal distribution No skew A normal distribution is not skewed it is perfectly symmetrical and the mean is exactly at the peak Positive skew It is when the long tail is on the positive side of the peak, and some people say it is “skewed to the right “ Negative skew A Negative skew is when the long tail is on the negative side of the peak, people say it is “ skewed to the left” Ms. Lubna Ineirat 66
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