Lecture and Lab Set on Descriptive
Statistics
What is descriptive statistics, broadly speaking? Why would we want to use descriptive statistics? -
correct answer ✔✔- With descriptive statistics, we have a numerical or quantitative summary of the
characteristics of a data set.
- We want to work with descriptive statistics because a simple summary is more efficient and effective
than a large set of values.
What are the two main ways we want to summarize data? Describe them. - correct answer ✔✔-
Measures of central tendency: the center of a data distribution given a group of data.
- Measures of dispersion: measure the spread of a data distribution given a list of data
These both are forms of summary. They help us BETTER UNDERSTAND our data from a broad point of
view.
What is a mode? Describe multimodal, bimodal, etc. - correct answer ✔✔Given a list of data, for any
value, if the value occurs most frequently, the value is the mode.
>>> Bimodal: two peaks
>>> Multimodal: multiple peaks
We don't always have a mode!
What is the median? How do we go about determining the median? - correct answer ✔✔The median is
the middle value from a set of ordered values - it is the VALUE with an EQUAL NUMBER of data above
and below it.
How do we determine the median?
, 1. Order data from smallest to largest FIRST.
2. If the number of values (n) is odd, median is the middle number in the list of ordered values.
Essentially, it should be at position (n+1)/2.
3. BUT, if the number of values (n) is even, then our median is the average of the middle two values.
What is the mean? What is the difference between the sample and population means? - correct answer
✔✔- The mean itself is the sum of the values divided by the number of values.
- The sample mean is the mean of observations. It is X BAR.
- Population mean is MU.
What is weighted mean? What does "weight" mean here? - correct answer ✔✔A weighted mean is a
meal where there is some variation in the relational contribution of individual data values to the mean.
Ex: GPA. wi is the weight of an observation (let's say a 3-credit class). xi is the value of that observation
(like 3.5). So, We must ADD the PRODUCTS of Wi and Xi - not just the SUM of Xi. Then we DIVIDE by the
sum of the wis.
What is range? - correct answer ✔✔Range is the difference between the largest and smallest values in
an interval/ratio set of data.
What is quantile deviation? - correct answer ✔✔Quantile means equal portions of a data set. There are
several types of quantile:
>>> Median: divide data into 2 EQUAL sets.
>>> Quartiles: 4 equal sets - 25%
>>> Quintiles: 5 equal sets - 20%
>>> Percentiles: 100 equal sets - 1%
A quantile gives lots of information, including the median. The median is a data value at the middle
position. Since the median is a value that to the left side and to the right side we have an equal number
of values, then median has 50% of values to the left of it and 50% of values to the right of it.
Statistics
What is descriptive statistics, broadly speaking? Why would we want to use descriptive statistics? -
correct answer ✔✔- With descriptive statistics, we have a numerical or quantitative summary of the
characteristics of a data set.
- We want to work with descriptive statistics because a simple summary is more efficient and effective
than a large set of values.
What are the two main ways we want to summarize data? Describe them. - correct answer ✔✔-
Measures of central tendency: the center of a data distribution given a group of data.
- Measures of dispersion: measure the spread of a data distribution given a list of data
These both are forms of summary. They help us BETTER UNDERSTAND our data from a broad point of
view.
What is a mode? Describe multimodal, bimodal, etc. - correct answer ✔✔Given a list of data, for any
value, if the value occurs most frequently, the value is the mode.
>>> Bimodal: two peaks
>>> Multimodal: multiple peaks
We don't always have a mode!
What is the median? How do we go about determining the median? - correct answer ✔✔The median is
the middle value from a set of ordered values - it is the VALUE with an EQUAL NUMBER of data above
and below it.
How do we determine the median?
, 1. Order data from smallest to largest FIRST.
2. If the number of values (n) is odd, median is the middle number in the list of ordered values.
Essentially, it should be at position (n+1)/2.
3. BUT, if the number of values (n) is even, then our median is the average of the middle two values.
What is the mean? What is the difference between the sample and population means? - correct answer
✔✔- The mean itself is the sum of the values divided by the number of values.
- The sample mean is the mean of observations. It is X BAR.
- Population mean is MU.
What is weighted mean? What does "weight" mean here? - correct answer ✔✔A weighted mean is a
meal where there is some variation in the relational contribution of individual data values to the mean.
Ex: GPA. wi is the weight of an observation (let's say a 3-credit class). xi is the value of that observation
(like 3.5). So, We must ADD the PRODUCTS of Wi and Xi - not just the SUM of Xi. Then we DIVIDE by the
sum of the wis.
What is range? - correct answer ✔✔Range is the difference between the largest and smallest values in
an interval/ratio set of data.
What is quantile deviation? - correct answer ✔✔Quantile means equal portions of a data set. There are
several types of quantile:
>>> Median: divide data into 2 EQUAL sets.
>>> Quartiles: 4 equal sets - 25%
>>> Quintiles: 5 equal sets - 20%
>>> Percentiles: 100 equal sets - 1%
A quantile gives lots of information, including the median. The median is a data value at the middle
position. Since the median is a value that to the left side and to the right side we have an equal number
of values, then median has 50% of values to the left of it and 50% of values to the right of it.
