Transcript How to Describe Data

Do Now
 Consider statistics. How is it relevant to real-life?
What are some applications we can use it for? Give
examples.
Think
 Looking at the data your class provided based on
time to break toothpicks, what do you think the
average time is for non-dominant hands?
 How big is this population?
 2 min
How to Describe Data

Today We Will…
 Determine how to calculate mean, median, range,
and mode of a data set
 Determine how to calculate standard deviation
Mean
 You calculate the mean (also referred to as the average
or arithmetic mean) by summing all the data points in
a data set (ΣX) and then dividing this number by the
total number of data points (N):
this is the sample mean
 What scientists want to understand is the mean of the
entire population, which is represented by μ. They use
the sample mean, represented by 𝑥̅, as an estimate of
μ.
 Again, our sample gives us the best representation of
our POPULATION
Example: Mean
 Students in a biology class planted eight bean seeds
in separate plastic cups and placed them under a
bank of fluorescent lights. Fourteen days later, the
students measured the height of the bean plants
that grew from those seeds and recorded their
results in Table 1.
Mean—example
 Find the sum of the heights: 7.5 + 10.1 + 8.3 + 9.8 +
5.7 + 10.3 + 9.2 + 8.7 = 69.6 centimeters
 Count the number of height measurements: There
are eight height measurements.
 Divide the sum of the heights by the number of
measurements to compute the mean: mean =
69.6 cm/8 = 8.7 centimeters
Mode
 The mode is another measure of the average. It is the
value that appears most often in a sample of data.
 It can be useful in describing some distributions.
 When is it ok to use which one?: using the mean is
most appropriate when you have a normal distribution
i.e one that follows a bell-shaped curve
 When our data is not normally centered—we can use
the mode, this allows us to see a cleared picture if our
data is skewed aka not centered or a bell-shaped curve.
Median
 The median is the data that falls directly in the
center. If we were to list our data points in
ascending order, we would find the number that
lies directly in the center of our distribution.
 Simply place the numbers in order and count the
number that is directly in the middle of the list
Range
 The range tells us our spread: what is the
difference between the highest and lowest
number in our data set?
 1. Identify the largest and smallest values in the
data set
 2. To determine the range, subtract the smallest
value from the largest value: range = 10.3
centimeters – 5.7 centimeters = 4.6 centimeters
Range cont’d
 For any data, a larger range value indicates a
greater spread of the data—in other words, the
larger the range, the greater the variability
Do Now
 Calculate the mean, median, mode, and range of
the following data set:
 45, 60, 96, 22, 33, 45,67 45, 88, 97, 36,56, 52
Toothpicks
 How long will it take you to break 10 toothpicks
with your non-dominant hand? Time your partner
before doing your own investigation?.
 Then when you’re done, break the 10 toothpicks
with your dominant hand
 Time yourself and place the time you got on the
board in seconds.
Today we will…
 Determine how to calculate standard deviation
Standard Deviation
 The standard deviation provides a measure of the
spread of the data from the mean.
 The sample standard deviation is an estimate of the
standard deviation in the larger population.
Standard Deviation

Steps:

1. Calculate the mean (𝑥) of the sample.

2. Find the difference between each measurement (xi) and the sample mean (ximean )

3. Square the difference (xi-mean)2

4. Add up (sum, Σ(xi- )2 all the squared differences

5. Divide by the degrees of freedom, which is 1 less than the sample size (n-1)

6. Take the square root

Sample standard deviation can either increase or decrease as a sample size gets
larger.
Stdev Example
The following table shows the frequency and salary of 20 people total. Using
the data table below, calculate the mean, median, mode, range, and standard
deviation
Follow with example on the board.
Salary
Frequency
$3500
5
$4000
8
$4200
5
$4300
2
Active Practice

1. The batting averages for 10 members of a baseball team are
0.234, 0.256, 0.321, 0.333, 0.290. 0.240, 0.198, 0.222, 0.300, and
0.276. Find the median batting average. Compare your mean to
your median, which is larger?

2. One of the events in the Winter Olympics is the Men’s 500meter Speed Skating. The times for this event are show to the
right. Find the mean, median, and mode times. Find the range
of the data set.

3. Look at your class data for the amount of time it took you and
your classmates to break apart toothpicks with both their
dominant and non-dominant hand. Calculate the mean, standard
deviation, and range. Compare the two data sets and describe
any variability that may have affected your standard deviation
for both sets. Are there any patterns worth noticing, why?
Exit Slip
 20, 24, 32, 22, 23, 32, 25
 The numbers above are the ages for tenants within
a building.
 Find the mean, median, mode, range, and
standard deviation for the particular data set of
ages. Make sure you specifically state the units
(age).