Question

Date:06/15/2020 Introduction: Use the same scenario you submitted for the first assignment with modifications using your instructor's feedback, if needed. Include Table 1: Variables Selected for the Analysis you used in Assignment #1 to show the variables you selected for analysis Table 1. Variables Selected for the Analysis Variable Name in data Description set Type of Variable (Qualitative or Quantitative) Variable 1: "Income" Quantitative Annual household income in USD Variable 2: Variable 3: Variable 4 Variable 5 Data Set Description and Method used for Analysis:

Answer 1

Mean — — -it is simple average.
Mean can be calculated by adding all the component and then dividing by the number of component.

$1*HlbbmmRf91Loy36pncS6Bw.png?q=20$

Here from above screenshot we can say that price at new york city is twice the price of los angeles because of that one price i.e 66 is affect in the mean value.

So, from that we can say that the mean is not enough to make definite conclusion.

But to overcome this we can calculate median value.

Median —- Median is the number at position (n +1)/2 in the ordered list.

Mode — — The mode is the value that occurs most often.

we can say mode of the pizza is 3 doller in new york city because it is most occur value in the list of new york city.

But in the list of los Angeles there is no any value often mostly occur repeatedly so there is no mode in that list.Each price occur only one time.
we say that there is no mode.OR We can say that 10 mode

But a experienced statistician will never do this.he will always say there is no mode.

Which measure is best?
-There is no best, but using only one definitely the worst!

Measures of Dispersion/Spread

Let’s take another example to understand this concept. We are talking salary data from some random Company A and B. For simpler statistics to understand, Central tendency parameters i.e. Mean and Median are almost similar for Company A and B.

However, we can see that the spread of salaries in company B is greater than that of company A. Based on this we can’t conclude if the salary for the company follows the same mean range pattern or not. So how does one translate this difference in spread into some meaningful descriptive statistic? Let’s walk through some of these descriptive terms we use in statistics to analyze our data:

1. Range: Range is the difference between the maximum and minimum value in a dataset. Lower the range of a dataset means less dispersion, and higher the range of dataset means greater dispersion.

Excel Command: “=MAX(number1,number2,….) — MIN(number1, number2,…)”

The maximum salary for company A is $100,100 and the minimum is $79,000, giving the range of $21,100. The maximum salary for company B is $111,000 and the minimum is $65,000, giving the range of $46,000. We can now confidently say that a higher range drives the greater spread in the data.

2. InterQuartile Range (IQR): Interquartile range is a widely used parameter in advanced statistical analysis. Before we go further let’s get our understanding clear about Quartile. Quartile divides the data into four equal parts in ascending order. This helps us to visualize the data in different ranges. They are denoted by Q0, Q1, Q2, Q3, and Q4 respectively.

Q0 = Minimum number in a data series

Q1 = Middle value in the first half of the data series in ascending order

Q2 = Median value of data series

Q3 = Middle value of the second half of the data series in ascending order

Q4 = Maximum number in a data series

Excel Command = “QUARTILE.INC(array, quart)”; Array is data series, and Quart is the quartile that we want to compute from 0 to 4.

We can also compute quartile 0, 2, and 4 with already learned excel commands before:

Q0 = “MIN (array)”;

Q2 = “MEDIAN(array)”;

Q4 = “MAX(array)”

Let’s understand this concept with this visualization and also define Interquartile range (IQR) as:

Interquartile range (IQR) = Q3- Q1

Excel Command = “QUARTILE.INC(array,3) — QUARTILE.INC(array,1)”

When we compute the IQR range for Company A and B respectively, it comes out at $7,500 and $14,675. Computing Median +/- IQR range gives a better idea about the sample population data by avoiding outliers, which we can’t be achieved by Range.

So, now we have learned about Range and IQR but which one is more preferred? IQR is often seen as a better measure of a spread than the range as it is not affected by the outliers. In a real-life scenario, instead of performing analysis on the entire population, we always prefer to take sample data as it is less costly. This sample data can be collected from IQR to get precise and clean statistics.