Stat help need

Open the Excel data file in the Week 8 folder. Your spreadsheet should like this:

This week we will complete the calculation and explanation of descriptive statistics with the help of Excel. Below are the commands needed to compute the respective values.

Measures of Variability/Dispersion1:

Min. Max. Range Variance Standard Deviation Quartiles:

Q1: Q3:

=min(array of values) =max(array of values) =(Max-Min) =VAR.P(array of values)2 =STDEV.P(array of values)

=QUARTILE.INC(array of values, 1)3 =QUARTILE.INC(array of values,3)

1 In order to calculate the Range in Excel, we need to calculate the High and Low value(s) in the data set(s). 2 In Excel, like all statistics programs, you have the option of calculating some measures for a “sample” or for a “population”. We are going to use the Population form. The alternative form of the function in Excel for variance and standard deviation would have “.S” instead of a “.P”. 3 In Excel, there is the option to INClude the median the calculation of the quartiles or EXClude the median. Including, as we have done, will affect the Q1 and Q3 calculations and provide more symmetrical quartiles. The disadvantage to this is that it will make it more difficult to identify outliers. Thus, we assume more normality in our distribution.

Assignment 2

IQR4:

McCormack CRIM.3950.01

Normality: Skewness:

Kurtosis:

=(Q1-Q3)

=SKEW.P(array of values)

=KURT(array of values)

The measures of skewness and kurtosis may be unfamiliar and/or new to you. These values can also be used to describe how normally distributed a set of data is. Each also has a threshold - or rule of thumb - value, which one can use to determine how normal (or not) a distribution is. Skewness measures the symmetry of the distribution. The closer the value is to 0 the more symmetrical the distribution is, e.g. the less skewed. The value measures the relative size of the two tails. Data that has skewness measured greater than | 1 | are highly skewed (positive or negative direction indicates the direction of the skew). Kurtosis measures the “peakedness” of the distribution. Excel calculates this value using the “minus 3” rule - a correction that actually reflects a normal distribution with a value of 0. Thus, in Excel, the closer the value is to 0, the more normally distributed the distribution is. Both values, like many of our descriptive measures, are heavily influenced by our sample size.

Like before, add these measures in the Excel spreadsheet. Begin below “mean”, in cell A49. Your spreadsheet should look like this (open your previous assignment if needed):

Using the commands above, let’s calculate the values. Ultimately, you should come up with the following values – formatted in tabular form:

4 The Interquartile Range (IQR) describes where the middle 50% of the data is located.

Assignment 2

McCormack CRIM.3950.01

All Reported Crimes

Annual Number in Boston 1985-2014

Mode N/A (multimodal) Median 35,788 Mean 43,069 Min. 22,018 Max. 70,003 Range 47,985 Variance 258,567,142.6

Standard Deviation Q1 Q3 IQR

Skewness Kurtosis

16,080.02 31,718.75 56,188 24,452.25 0.47 -1.27

How would we explain these results? First, we see a fairly large range. Annually, we have seen a near consistent decrease in the overall number of reported crime in Boston. Its peak was in 1989, with just over 70,000 crimes reported, and a low in 2014, with just over 22,000 crimes reported. With a large range usually comes a large standard deviation. A value of just over 16,000 indicates that the typical distance each annual total is away from the mean is about 16,000. So, the annual values tend to differ. We know the IQR represents where the middle 50% of the data lie, so half of all years had between about 31,000 and 56,000 reported crimes.

Variability and Dispersion

Calculate the measures of variability and dispersion for the same 3 offenses you have worked with previously. Create a similar table for those same 3 offenses.

Copy/paste them into or create in a Word document (.doc or .docx) which will be submitted.

Beneath each table (3 you picked and created), write a 100-word paragraph describing the measures of variability and dispersion.

Ensure all of your tables and write-ups are submitted in one Word (.doc or .docx) file for Assignment 3.