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

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

2 S1 Measures of Dispersion Objectives: To be able to find the variance and standard deviation for discrete and continuous data using excel

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

4 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 1.3, 9, 12, 24, 10, 21, 27, , 56, 61, 34, 50, 50, 66, 51, 48, 49, , 22, 30, 27, 19, 25, 2, 156 Compare the answers you got in Q1 and 2 to the answer for Q3. Explain the difference

5 The variance and standard deviation from a frequency table fx Number of rods (x) Freq of rods (f) fx² Σf=109 Σfx=4096Σfx²= Variance = Σfx² – Σfx ² Σf Σf Variance = – 4096 ² σ ²= σ = 1.109

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

7 Variance and standard deviation from a grouped frequency distribution Height of plant (cm) Freq (f) 0 < h 54 5 < h < h < h < h < h 301 Total σ ² = – 285 ² = σ = σ = 11.35

8 Use excel to work out the standard deviation for the following sets of data XF XF HeightF HeightF 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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