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**S1 Measures of Dispersion The mean, variance and standard deviation**

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**S1 Measures of Dispersion**

Objectives: To be able to find the variance and standard deviation for discrete and continuous data using excel

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**The marks scored in a test by seven students are 3,4,6,2,8,8,5**

The marks scored in a test by seven students are 3,4,6,2,8,8,5. Calculate the variance and standard deviation. x 3 4 6 2 8 5 Variance = Σx² – Σx ² n n _ x² 9 16 36 4 64 25 σ ² = 218 – 36 ² = 4.69 σ = √4.69 = 2.17 Σx = 36 Σx² = 218

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**Variance and standard deviation of discrete data**

Variance = Σx² – Σx ² n n _ Use excel to quickly work out the variance and standard deviation of the questions below 3, 9, 12, 24, 10, 21, 27, 16 45, 56, 61, 34, 50, 50, 66, 51, 48, 49, 38 18, 22, 30, 27, 19, 25, 2, 156 Compare the answers you got in Q1 and 2 to the answer for Q3. Explain the difference

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**The variance and standard deviation from a frequency table**

Number of rods (x) Freq of rods (f) 35 3 36 17 37 29 38 34 39 26 fx fx² 105 612 1073 1292 1014 3675 22032 39701 49096 39546 Σf=109 Σfx=4096 Σfx²=154050 Variance = Σfx² – Σfx ² Σf Σf Variance = – ² σ ²= σ = 1.109

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**Use Excel to quickly work out the variance and standard deviation of the question below**

4 2 5 17 6 22 7 15 8 Variance = Σfx² – Σfx ² Σf Σf Change the frequency for x=4 or x=8. What happens to the standard deviation? What happens when you change the frequency when x=6? Explain why

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**Variance and standard deviation from a grouped frequency distribution**

Height of plant (cm) Freq (f) 0 < h ≤ 5 4 5 < h ≤ 10 15 10 < h ≤ 15 5 15 < h ≤ 20 2 20 < h ≤ 25 25 < h ≤ 30 1 Total σ ² = – 285 ² = σ = √ σ = 11.35

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**Describe the skewness of each of the data sets**

Use excel to work out the standard deviation for the following sets of data X F 8 13 9 21 10 37 11 35 12 4 X F 23 127 24 90 25 56 26 17 27 8 Height F 5-10 6 11-16 15 17-22 21 23-28 56 29-34 52 Height F 25-34 20 35-44 24 45-54 37 55-64 42 65-74 22 75-84 16 Comment on and compare the standard deviation for each of the data sets Describe the skewness of each of the data sets

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