# You were randomly assigned a city - BEIJING - and a period of the y...

## Question

You were randomly assigned a city - BEIJING - and a period of the year you must analyze - Winter. In particular, you are going to analyze the months of December, January, and February.
So, the first thing you need to do is to select the observations you need to analyze. You can do this in several ways, such as sorting the data by month, picking only the months you need and deleting the rest of the observations; or (probably quicker way) creating an indicator variable (in column E) that takes a certain value (for example, 1) if the observation is in your period of analysis and another value (say, 0) otherwise. You create this indicator variable using the IF function in Excel. Once that variable is created, sort the observations by that indicator variable and delete all the observations that are not in your period (observations for which the indicator variable is 0).
If you did things correclty, you should be left with 1,955 observations. Make sure to confirm that you have this number of observations, as the answers to the questions will not be right if you don't have the correct data. For the next 9 questions, I will ask you to enter descriptive statistics - measures of location and center. Use the Excel functions to compute them.
What is the mean daily temperature? (Round your answer to one decimal point)

Question 2
What is the median daily temperature? (Round your answer to one decimal place)

Question 3
What is the lower quartile? (Round your answer to one decimal point)

Question 4
What is the upper quartile? (Round your answer to one decimal point)

Question 5
What is the range of daily temperatures? (Round your answer to one decimal place)

Question 6
What is the Mean Absolute Deviation of the daily temperatures? (Round your answer to two decimal places)

Question 7
What is the Mean Squared Deviation of the daily temperatures? (Round your answer to two decimal places)

Question 8
1. What is the variance of the daily temperatures? (Round your answer to two decimal places)

Question 9
What is the standard deviation of the daily temperatures? (Round your answer to two decimal places)

Question 10
You want to describe your data using a table. You decide to divide the data into 9 equally spaced intervals. The width of each of your bins is 5.5 degrees Farhenheit. The lower bound of your first bin is 4.75. Show, in a table, the intervals, the cell midpoints, the frequency and the relative frequency. When you compute the frequency, you can use the Excel functions COUNTIF() and COUNTIFS(). That is the easiest option. Alternatively, you can use the array Excel function FREQUENCY(). Array functions are a bit harder, but the example used in the Excel tutorial session should have instructions on how to use it. So that the answers using Frequency or Countifs are the same, make sure to when you use COUNTIF and COUNTIFS, you follow these rules:
First bin of your table - Count all the values lower than or equal to the upper bound of the first interval
Last bin of your table - Count all the values higher than the lower bound of the last interval
All the other bins in your table - Count all the values that are higher than the lower bound and lower or equal to the upper bound of the interval.
After you create your table, draw the corresponding histogram.
Please submit your histogram here. You should copy the histogram created in your excel spreadsheet and save it as a picture (.png) or paste it into a word document and submit your .doc file. You can also submit your histogram as a .pdf.

Question 11
Now, assume that the only information given to you was the nine-bin frequency table you computed in the question above - assume you DO NOT have the original observations. Recompute the mean, using the formula you learned for grouped data. What is the value of the mean, using the grouped data? (Round your answer to one decimal place)

Question 12
Using the information contained in your table only, compute the median, using the more sophisticated approximation (presented in lectures). Enter your answer rounded to the nearest one decimal place.

Question 13
Using the information contained in your table only, compute the lower quartile, using the more sophisticated approximation (presented in lectures). Enter your answer rounded to the nearest one decimal place.

Question 14
Using the information contained in your table only, compute the upper quartile, using the more sophisticated approximation (presented in lectures). Enter your answer rounded to the nearest one decimal place.

Question 15
Using the information contained in your table only, compute the variance. Round your answer to the nearest two decimal places.

Question 16
Based on the information on the table, what is the standard deviation of your data? Round your answerto the nearest two decimal places.

Question 17
Compare the descriptive statistics computed using the original observations, and the ones computed using the grouped data. Fill in the blank: "The descriptive statistics using the original observations are fairly [A] (similar to / different from) the ones computed using grouped data."

Question 18
Create a box plot either using the descriptive statistics you found using the grouped data or the ones you computed using the original observations. I posted on TritonEd a template that will help you draw box plots – Its name is boxplot_template.xls. Once you created the box plot, click on it and save it as an image (.png). Submit your box plot here.

Question 19
Continue to assume that you only have the information in the table (the grouped data). You go to Europe, and you want to present your data in Celsius. Knowing that C = (F - 32) * (5/9), where F is the temperature in Fahrenheit and C is the temperature in Celsius, what is the average daily temperature of your city for your period of analysis, in Celsius? (Try to use Excel to make this computation, although any calculator would work for this question). Present your answer rounded to one decimal place.

Question 20
Continue to assume that you only have the information in the table (the grouped data). You go to Europe, and you want to present your data in Celsius. Knowing that C = (F - 32) * (5/9), where F is the temperature in Fahrenheit and C is the temperature in Celsius, what is the standard deviation of the daily temperature of your city for your period of analysis, in Celsius? (Try to use Excel to make this computation, although any calculator would work for this question). Present your answer rounded to two decimal places.

Question 21
Please submit your Excel file here. Your Excel file should contain the computations you did to answer the questions above. In particular, it should contain the excel functions you used to compute the descriptive statistics, the table you created grouping the data, the histogram and the statistics you computed using the grouped data.

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