This document discusses various statistical concepts and analyses movie data using different statistical methods. It defines statistical terms like mean, median, mode, midrange, range, and variance. It then calculates these values for movie runtimes and revenue. Various graphs are presented to visualize the movie data, including a box and whisker plot showing an outlier, a frequency bar graph of movie ratings, and a stem and leaf plot of movie revenue. Examples are provided of calculating mean, median, mode, midrange, and range for a sample data set.

1. Anilu Mendiola | Milestone 1 | Math 115
Favorite Movies
Statistics

2. THE DATA :
Reference: https://m.imdb.com/
Quantitative Data Quantitative Data Qualitative Data

3. Mode: The mode is the most common number in a data
set.
Midrange: The average of the largest and smallest data
points. To find the midrange, add together the least and
greatest values and divide by two.
Range: : The range is the difference (subtraction) between
the largest number and smallest number of a data set
Mean: Used to calculate the average. It is found by
adding up all the values in a set of data, then dividing
that total by the number of values there were in the data
set.
Median: The median is the middle number of a set of
values.
MEAN, MEDIAN,MODE,MIDRANGE,RANGE

4. VARIANCE : MOVIE RUNTIMES
A variance is the average of the squared
differences from the mean. I gathered my
movie runtimes and placed them in order from
lowest to highest in this chart.
First I calculated the Mean (139.7). Then you
take each value in data set, subtract the
mean(second column) and square the
difference (Third column). Then add the
squared differences for all values (SS= 8864.1).
The sum is then divided by the number of
values (8864.1/10= 886.41). The variance is
886.41

5. STANDARD DEVIATION
The formula we use for standard deviation depends on whether the
data is being considered a population of its own, or the data is a
sample representing a larger population.
-If the data is being considered a population on its own, we divide
by the number of data points, N.
-If the data is a sample from a larger population, we divide by one
fewer than the number of data points in the sample, N−1.
For this particular data I used the Population Standard Deviation.
From our example of the previous slide our Variance was 886.41
Find the square root of the Variance to determine the Standard
Deviation.
σ = 886.41 = 29.772638

6. BOX & WHISKER PLOT
Box & Whisker Plot shows how your data is spread out and it’s also useful because it shows outliers within a dataset. I used the 5
number summary (Minimum, Q1, Median (Q2), Q3 and the Maximum) to create this graph.
Using the 1.5*IQR Rule I determined that there is a outlier in my dataset. Q3-Q1 (152-130=22) 22*1.5=33
152+33= 185 then 130-33=97 therefore the range of “normal data” is 97 to 185.
Data: (81,105,130,132,142),(143,149,152,169,194)
Median= 143+142 /2 =142.5
Minimum Q1 Q3 Maximum

7. FREQUENCY BAR GRAPH
DATA SET:
A Frequency Bar Graph shows the frequencies of
each category accumulated together.
This graph allows me to analyze the distribution of
the data in more detail. It can also compare various
sets of data.
I took the star ratings and put them into a frequency
table. I was able to determine the number of times a
star rating is repeated.
This is a Vertical Frequency Bar Graph. I included the
title, the X axis and Y axis , equal interval spacing
and added different colors to the bars that are
vertical.

8. STEM AND LEAF PLOT- REVENUE
A Stem and Leaf Plot is a table where each data value is split into a
"stem" (the first digit or digits) and a "leaf" (usually the last digit).
Leafs need to be written in from the lowest to the highest value
It is used to represent data visually.
◦ Outliers
◦ Shape of data distribution
◦ Range
Data: 100,168,188,210,223,330,535,623,719
I took the Revenue of the 10 movies and rounded the
values to millions. Example: $100,234,567 to 100 millions.
I used two digits for the stem and one digit for the leaf. By
observing the data you can see that most data are
grouped in the lower range of the graph.

9. Calculate the Mean, Median, Mode, Midrange and
Range for this given data set: 3,3,5,6,7,8,10
Mean
•1. Add up all the numbers 3+3+5+6+7+8+10= 42
•2. Divide the total by the number of values in the
set. There are 7 numbers in the set. 42/7 = 6
The Mean would be 6
Median
•1. Arrange the numbers in order- smallest to largest.
3,3,5,6,7,8,10
•2. Identify the middle number : Median= 6
Mode
•The value that appears most often is 3
Midrange
•Add the least and greatest values together and
divide by two. 3+10 = 13 13/2= 6.5
Midrange=6.5
Range
•Subtract the large value from the smallest
value. 10-3= 7
The range is 7