Chapter 3: Frequency Distributions
3.1 Qualitative Frequency Distribution and Histogram
(qualitative data)
Learning Activity 3.1-1 Qualitative Frequency Distribution
 Open RealEstateData.xls!Data
 Use the MegaStat | Frequency Distributions | Qualitative
K2:K126 as input range and N5:O9 as specification range
 Change the title to “Percent of House in Each Subdivision.”
 Modify the chart by right-clicking one of the histogram bars,
| 資料數列格式 | 填滿
 Rerun using N19:Q20 as the specification range.
Learning Activity 3.1-2: Region.xls!Data
Learning Activity 3.1-3: Poll1.xls!Data
“There are three kinds of lies: lies, damned lies and statistics.”
Learning Activity 3.1-4 How to lie with statistics
(scaling histogram)
 Use the output from Learning Activity 3.1-1.
Right-click the vertical axis
Select 座標軸格式
Click the 刻度and type in the minimum and maximum values
Use 0 and 100
Use 10 and 32
Note: When you see a histogram or any graphs, look at the
scaling.
3.2 Quantitative Frequency Distribution and Histogram
Determine Interval Width and Setup Intervals
1. Calculate the range of the data
2. Determine an approximate number of intervals, k.
Use EXCEL function to find k~=LOG(data number,2)
3. Use a round number of range/k as your interval.
A round number is an even multiple of power of 10
times 1, 2, or 5, e.g. 45.4 would be 50.
4. MegaStat will set up the intervals for you.
2k
k
16
4
32
5
64
6
128
7
256
8
512
9
1024
10
Your sample size
~ 2k, then K is your
number of intervals.
Learning Activity 3.2-1 Frequency distribution, histogram
 Open RealEstateData.xls!Data.
 Use MegaStat|Frequency Distributions|Quantitative
Specify the Price variable (B2:B126) as the input range.
Type 100 as the interval width
 Rerun, specifying 10 as the interval width
 Rerun, specifying 250 as the interval width
 Let the MegaStat chose the interval width
Learning Activity 3.2-3 Frequency distribution, histogram
 Open a new Excel workbook.
 Use MegaStat|Generate random Numbers
Number of values: 600
Decimal places: 2
Use fixed values
Select a distribution and specify the required inputs
 Determine the appropriate interval width and set up the
interval
 Use MegaStat|Frequency Distributions | Quantitative (specify
Histogram, Polygon, and Ogive).
The ogive plots the cumulative percents. It can be used to
estimate quartiles.
Exercises: Ch_03_Frequency_dist,xls in the exercise folder of
the CD.
3.B Capping the top interval
Go to GPAdata.xls and use MegaStat to find the histogram.
Compare your histogram to that in the Capped Top Interval.
3.C Estimating the Median and Quartiles from a Frequency
Distribution
1

n

CF


Interpolated Median = L  w 2 f 




Where:
L = lower limit of the interval containing the median
w = width of interval
n = total sample size
CF = cumulative frequency below the median interval
f = frequency of the median interval
Changing 1/2 to 1/4 or 3/4 and L, CF and f,
you can calculate quartiles.
L
w
f
CF
1

1

n

CF
124

38
2

2

Interpolat ed median  L  w 
 300  50 
 344.444


f
27








Try to calculate the Q1 and Q3.
Estimating the Median from a Cumulative Distribution (Ogive)
Ogive
Cumulative Percent
100.0
75.0
50.0
25.0
0.0
150
250
350
Price
About 345
450
550