Chebyshev\'s Theorem: Th e proportion (p) of data points that is within k standa
ID: 3058235 • Letter: C
Question
Chebyshev's Theorem: Th e proportion (p) of data points that is within k standard deviations of the mean is at least given by the formula: p- Exumple 13: (a) Calculate the percentage (p) of data points that is within k-3 Use Chebyshev's theorem with X 68, n-85 and S-10 and do questions a -d deviations of the mean write p as a percentage to one decimal place. p = e Substiture the given value of k into Chebyshev's formula and evaluate p p 75% of the data. First convert 75% to a decimal, k = o Substitute tihe given value of p into Chebyshev's formula and soive for k (o) Find the number of standard deviation (k) on either side of the mean that cuts off ( 0 ) ag ) (c) Find the interval on which at ieast 75% of the data lies: kS . The interval on which at least the proportion p values exist is given by: X . Use the correct value of k calculated in part (b) above The lower limit must be written first in interval notation L oy. (d) At least how many values fall within this interval: n· n·= p . n. If you get a fraction t round up to the nearest whole number Example 14: Convert the scores to standard z-scores and state which student has the best sc Answer questions a - e below and write Z scores to 2 decimal places. (a) Mary's grade is 75, class mean-68 and elays standard deviation-8; (b) lohn's grade i, 80, class mean-7 and class standard deviation= 142- o) Mar's gade is 90, class mexg 14pup class sandard a mea10-1asshandarddeviation-10, z.LOO 90, class mean 74 and class standard deviation 10;2 d) Sue's grade is 85, class mepn 62 and class standard deviation-12;2 (e) Which student has the best score?Explanation / Answer
Chebyshev's Theorem: Th e proportion (p) of data points that is within k standard deviations of the mean is at least given by the formula: p- Exumple 13: (a) Calculate the percentage (p) of data points that is within k-3 Use Chebyshev's theorem with X 68, n-85 and S-10 and do questions a -d deviations of the mean write p as a percentage to one decimal place. p = e Substiture the given value of k into Chebyshev's formula and evaluate p p 75% of the data. First convert 75% to a decimal, k = o Substitute tihe given value of p into Chebyshev's formula and soive for k (o) Find the number of standard deviation (k) on either side of the mean that cuts off ( 0 ) ag ) (c) Find the interval on which at ieast 75% of the data lies: kS . The interval on which at least the proportion p values exist is given by: X . Use the correct value of k calculated in part (b) above The lower limit must be written first in interval notation L oy. (d) At least how many values fall within this interval: n· n·= p . n. If you get a fraction t round up to the nearest whole number Example 14: Convert the scores to standard z-scores and state which student has the best sc Answer questions a - e below and write Z scores to 2 decimal places. (a) Mary's grade is 75, class mean-68 and elays standard deviation-8; (b) lohn's grade i, 80, class mean-7 and class standard deviation= 142- o) Mar's gade is 90, class mexg 14pup class sandard a mea10-1asshandarddeviation-10, z.LOO 90, class mean 74 and class standard deviation 10;2 d) Sue's grade is 85, class mepn 62 and class standard deviation-12;2 (e) Which student has the best score?