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STATISTICS AND NUMERICAL METHODS MATH 0102 Measures of Central Location

STATISTICS AND NUMERICAL METHODS MATH 0102 Measures of Central Location. Mean (Ungroup data). called the arithmetic mean , by sharing the sum of the quantities concerned equally between the numbers of quantities. RULE : add up the data provided and divide by the number of quantities.

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STATISTICS AND NUMERICAL METHODS MATH 0102 Measures of Central Location

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  1. STATISTICS AND NUMERICAL METHODSMATH 0102Measures of Central Location NURAZRIN JUPRI

  2. Mean (Ungroup data) • called the arithmetic mean, • by sharing the sum of the quantities concerned equally between the numbers of quantities. • RULE: add up the data provided and divide by the number of quantities. NURAZRIN JUPRI

  3. Example: What is the arithmetic mean of the monthly takings? An investigation into the takings of a small grocer’s shop gives the following results:   £ • January 2 794 • February 1 986 • March 2 325 • April 3 654 • May 3 726 • June 3 985 • July 6 574 • August 7 384 • September 5 259 • October 3 265 • November 4 381 • December 5 286 £50 619 NURAZRIN JUPRI

  4. Median (Ungroup data) • Median: that value which divides the data into two equal halves; 50% of values lying below and 50% above the median. • Array: place data in numerical order – whether rising or falling • Median positionis n + 1 2 where n = number of values • Median valueis that value which corresponds to the median position NURAZRIN JUPRI

  5. The median is the value of the middle item of a distribution once all of the items have been arranged in order of magnitude. • The median of the following nine values: 26 4 24 11 12 28 86 90 2 • The median of the following ten values: • 26 4 24 11 12 28 86 90 2 8

  6. TRY! • Model A: 1, 2, 18, 23, 26, 42, 294 • Model B: 43, 44, 45, 69, 73, 76 Find the median? NURAZRIN JUPRI

  7. Mode (Ungroup data) • Mode: that value which occurs most often (i.e. with the highest frequency) • Example: • 1 2 1 2 3 4 6 1 2 2 7 • 1 2 1 2 4 1 1 2 2 7 • 1 2 3 4 9 5 6 8 7 NURAZRIN JUPRI

  8. Example: NURAZRIN JUPRI

  9. Example: central location for ungrouped data • The following data measures the attention span in minutes of 15 undergraduates in a sociology lecture. 4, 6, 7, 8, 8, 8, 8, 9, 9, 10, 11, 12, 14, 15, 18 • Find the arithmetic mean • Find the median • Find the mode

  10. Central location: grouped data • Grouped data: data which is only available in grouped form e.g. class intervals in frequency table • Class mid-points: we assume that the data in any class interval all fall on the class mid-point. Put another way, the data are equally spread along any given class interval

  11. Mean (grouped data) • Where Fi = frequency of ith class interval Xi = mid-point of ith class interval j = number of class intervals Note: simplifying assumption: all values in a class interval are equally spread along that interval

  12. Find arithmetic mean of grouped data • Find mid-point of each class interval. Arithmetic mean x = ∑ fx / ∑f = 224/ 18 = 12.4units

  13. Median (grouped data) LCB = lower class boundary CF = the cumulative number of frequencies in the classes preceding the class containing the median F = the frequency of the median class NURAZRIN JUPRI

  14. Mode (grouped data) • Modal class interval: that class interval in which the mode value falls NURAZRIN JUPRI

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