Download Precalculus – Chapter 3: Section 3-1

Notes:
Precalculus – Chapter 13: Statistics and Probability
Section 13-2: Measures of Center and Spread (Page 853)
 Mean – commonly known as average. Add all values and divide by
the total number of values. Represented by x, x bar.
o Problem with mean – can be distorted by extreme values
 Median – middle value. Put values in numerical order. If there are
an odd number of values, the middle value is the mean, if there are an
even number of values, the median is the average of the two middle
values.
o More resistant measure of center than the mean since it is less
affected by extreme values
 Mode – data value with the highest frequency. Mostly used for
qualitative data, where there is no mean or median. (“most typical
value”)
o If every value occurs the same number of times, there is no
mode. If two or more have equal frequencies that are higher
than others, the data set is called bimodal (trimodal for 3 modes
or multimodal for more)
Median
Mode
mode
mode
median
median
mean
mean
mean
 variability – the spread of the data
 standard deviation – most common measure of variability. Best
used when the data is symmetric about the mean. Measures the
average distance of a data element from the mean.
o If data is taken from a sample instead of the population, it is
common to divide the variance by n-1 instead of n when
averaging the squared deviations. This is called the sample
standard deviation, denoted s.
o To find standard deviation: subtract each value from the
mean, square it, add for each value together, divide by n (or
n-1 for sample standard deviation) and take the square root.
 TI NOTE: Enter data into L1 (or other lists as long as you specify
when calculating). STAT. CALC. 1-Var Stats. ENTER. L1 (or other
if needed). ENTER.
o Shows mean, sum, sum squared, sample standard deviation,
standard deviation, number in set, minimum value, 1st
quartile, median, 3rd quartile, maximum value
 Range – difference between the maximum and minimum values
 Interquartile Range - measure of variability that is resistant to
extreme values
o 1st quartile – the median of the lower half of the values
o 3rd quartile – the median of the upper half of the values
o interquartile range – the difference between the quartiles.
This represents the middle 50% of the data.
 Box Plot (also known as box and whisker plot):
1. draw a number line and locate each value of the 5 summary
2. construct a rectangle whose length equals the interquartile range
with a vertical line indicating the median
3. Construct horizontal whiskers to the minimum and maximum
values (if there is an outlier, this can be marked with a star and
not included as part of the plot)
min Q1
25%
Hmwk
median
25%
Q3
25%
max
25%
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