Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

Measures of Central Tendency – statistics that describe the tendency of data to center about certain numerical values. – mean – median – mode Measures of Dispersion – describes (measures) how spread out the data is. – range – interquartile range – standard deviation Measures of Dispersion

Range the difference of the greatest and least values. Measures of Dispersion Range = Largest Value – Smallest Value The number of piglets in the litter of 10 pigs are: Find the range. 16 – 9 = 7

Interquartile Range the difference of the lower and upper quartiles. Measures of Dispersion IQR = Q 3 – Q 1 Find the interquartile range of the data set: – 6 = 5

Standard Deviation The most widely used measure of the spread of a sample. Measures the deviation between data values and the mean. – The larger the standard deviation, the more widely spread the data (and vice versa). Measures of Dispersion

{35, 40, 45} and {10, 40, 70} 40 is the mean of both sets, yet the variability is much greater in the second set than in the first. Compare:

x is any score is the mean n is the number of scores Standard Deviation Formula: Do not need to be able to solve by hand! Only need to be able to solve using GDC.

Calculate the standard deviation for the sample: 2, 4, 5, 5, 6, 6, 7 Need the mean, so calculate this first. Utilizing a chart can make calculations easier. Let’s try one by hand though: = 5

Calculate the standard deviation: Values Calculate the mean Subtract the mean from each value Square these Add them Divide by n Take the square root = 2.29 = 1.5

Find the mean and standard deviation on GDC: Type data in List 1 1-Var Stats L1 On paper you’ll see ‘s’ being used to standard for standard deviation. But you should use the σ measurement from the calculator.

Find the mean and standard deviation on GDC: Find the mean and SD of this data set: mean = 7 Standard deviation = 3.10

Find the standard deviation of a frequency table on GDC: Type data in L1 Type frequency in L2 1-Var Stats L1, L2

Find the standard deviation of the following distribution of scores. ScoreFrequency s.d. = 2.38

Find the standard deviation for the following distribution of examination scores. markfrequency Midpoint s.d. = 16.8