Chapter 3 ReviewMDM 4U

Mr. Lieff

3.1 Graphical Displays

be able to effectively use a histogram recognize and be able to interpret the various

types of distributions ex: when would we use a histogram vs. a bar

graph? ex: how do you calculate bin width?

3.2 Central Tendency

be able to calculate mean, median, mode and weighted mean ex: determine which measure is appropriate

be aware of the effect of outliers recognize the location of the measures with

respect to skewed distributions if mean > median…right skew if mean < median…left skew

3.3 Measures of Spread

be able to calculate IQR and population standard deviation

interpret the meaning of the values the larger the standard deviation, the larger

the spread of data IQR gives the range containing 50% of the

data what is the population standard deviation for:

3 5 7 8 8 9 10 12 14 ans: 3.166

3.4 Normal Distribution

be familiar with the characteristics of a normal distribution

use a normal distribution to calculate the ranges of expected data

ex: with a mean of 10 and a standard deviation of 2, how many percent of the data lie between 6 and 14?

ans: 95%, with a std dev of 2, 6 is 2 std dev below the mean and 14 is 2 above. So 95% of the data falls in the range (see diagram)

Normal Distribution

34% 34%

13.5% 13.5%

2.35% 2.35%

68%

95%

99.7%

x x + 1σ x + 2σ x + 3σx - 1σx - 2σx - 3σ

),(~ 2xNX

0.15%0.15%

3.5 Z-Scores

understand the use of the standard normal distribution

be able to calculate a z-score be able to calculate the percentile position of a piece

of data, given the standard deviation and the mean be able to calculate the percent of data in a range of

population values

)1,0(~ NX

xx

z

3.5 Z-Scores

ex: given a normal distribution with a mean of 10 and a std dev of 2, what percent of the population is between 7 and 11?

ans: calculate z-scores for the two data values and subtract their percentile positions

for 7: (7 – 10)/2 = -1.5 z = 6.68% for 11: (11-10)/2 = 0.5 z = 69.15% 69.15-6.68 = 62.47 so 62.47% lies between these two values

3.6 Mathematical Indices

these are arbitrary numbers that provide a measure of something

e.g. BMI, Slugging Percentage, Moving Average

you should be able to work with a given formula and interpret the meaning of calculated results