Statistics
Unit Plan (daily outcomes)
Assessments:
- Calculate and interpret mean (average), median, and mode to solve problems.
- Calculate and interpret standard deviation to solve problems.
- Use histograms and frequency polygons to represent distributions.
- Solving normal distribution problems.
Unit Plan (daily outcomes)
Assessments:
Measures of Central Tendency and Measures of Dispersion
- Central Tendency - mean (average, find the sum of data then divide by number of data items), median (middle, when data is organized from minimum to maximum) and mode (most frequent)
- Dispersion - range (difference between maximum value and minimum value) and standard deviation (measure the dispersion from the mean, we use the population formula).
- Lesson:
Calculator Skill Sheets:
Calculator Stat Videos (one variable stats, List 1):
Histograms & Frequency Polygons
SKILL BUILDING:
- We like to have a maximum of 10 intervals for our histograms. To determine the interval width, divide the range by the number of intervals you want to work with and round up to a nice number.
- Set up a tally chart (intervals, tally, frequency). Work through the data - tally the interval for each vale. Record tally value as a number.
- Set up the horizontal axis to represent the interval widths and the vertical axis for the frequency. Give your graph a title. Draw the bars for the histogram.
- Frequency curve
- Method 1: replicate the horizontal and vertical axis from the histogram; plot a point at the median value and frequency height for each interval; join the points (smooth or straight line)
- Method 2: place a point in the top middle of each interval on the histogram; join the points (smooth or straight line)
- Calculate the mean and standard deviation using data in a frequency table.
- List 1 is the median of each interval. List 2 is the frequency of each value.
- Tell your calculator to use L1 and L2 to calculate your 1-Variable Stats.
- Lesson
- Histograms and Frequency Polygons
- Notes and Examples
- Videos:
- Organized Data (data and frequencies):
- Two List Calculations: Original and Answer Key
SKILL BUILDING:
- Central Tendency, Dispersion & Histograms Assignment: original and Answer Key
Problem Solving - understanding Standard Deviation
- Find mean and standard deviation for a set of quiz scores.
- Interpret the results when extreme (lowest and highest) values removed on mean, median and standard deviation.
- Mean - usually change a small amount
- Median - does not change if equal number of low and high values are dropped from data set
- Standard Deviation - gets smaller as the remaining data values are all closer to the mean
- Calculate the mean and standard deviation using data in a frequency table.
- List 1 is the median of each interval. List 2 is the frequency of each value.
- Tell your calculator to use L1 and L2 to calculate your 1-Variable Stats.
- Lesson:
- Understanding Standard Deviation & Historgrams. (we reviewed finding mean and standard deviation by entering all data in a single list; we showed how to find the mean and standard deviation from a frequency table).
- Notes and Examples
- Videos:
SKILL BUILDING:
- Standard Deviation Assignment: Original and Answer Key
- More: mean, median, mode, standard deviation, frequency table & histograms. original and answer key
Normal Distributions - where the mean, the median and the mode are all equal with specific percentages of the population dispersed about the mean.
- Lesson
- Build Your Skills: practice skills finding mean, standard deviation and solving normal distribution problems:
- Original and Answer Key
Z-Scores: measure the distance from the mean in terms of deviations from the mean.
Lesson:
Z-score Problems: sketch a normal curve, identify z-scores (calculate them if required), shade area of curve, use normalcdf to find area between z-scores, use Inverse Normal and the area to the left to find a z-score.
- z-score Problems and Answers
Problem Solving:
Videos:
- Area between using z-scores
- Casio
- TI
Online Calculator (use to replicate your calculator):
- Online Statistics - Normalcdf
- Online Statistics - Inverse Normal
- SUBEDI - One Variable Stats (use population)
Statistics Review (old exam): original and answer key
Extra Practice (Problems for Practice: original and answer key)
Extra Practice (Problems for Practice: original and answer key)
2021