ANATOMY OF SUMMARY STATISTICS:
Measures of Central Tendency, Variation and Position
440
481
482
483
483
514
514
554
554
554
562
612
623
631
638
664
671
677
690
707
The Minimum is the
smallest value in a data set.
Mean: The mean of a data set, is the sum of all values in the
data set, divided by the number of values in the data set.
Here, the sum of all data values is 11534, and there are 20 data
values, therefore the mean is 11534/20 = 576.7 lbs.
The Mode is the most frequently occurring value
in a data set. Here the mode is 554 lbs. Note that
it is possible to have more than one mode in a data
set.*
Standard Deviation: The standard deviation is used in
conjunction with the mean. It represents a measure of distance
from a given value to the mean.
Median: The median is the value in the middle
position, in a data set that has been ordered from
smallest to largest. Here, the middle position is
between two values, therefore, we add the two values,
and divide their sum by 2. In this case, the median is
(554 + 562)/2 = 558 lbs.
Inter-Quartile Range: A measure of the middle 50% of a
distribution’s data. It is often used in conjunction with the
median as a measure of dispersion.
Range: The range of a data set is the difference between the
The Maximum is the
largest value in a data set.
*A data set containing two modes is called bimodal. A data set
containing more than two modes is called multi-modal.
maximum value, and the minimum value. Here, the range is 707
- 440 = 267 lbs.
Midrange: The midrange of a data set is the difference
between the maximum value and the minimum value, divided
by 2. Here the midrange is (707 - 440)/2 = 133.5 lbs.
The Data: The data set comes from Dudley’s Doughnuts. It is the amount
of flour (in pounds) used on each of 20 consecutive days in December 1999.
The data have been ordered from smallest to largest in value.