Math 1280 Assignment Unit 2, Exercises of Statistics

Math 1280 Assignment Unit 2 for reviewing purposes.

Typology: Exercises

2018/2019

Uploaded on 12/09/2019

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1. Sometimes it is difficult to understand data if you do not know what the numbers
represent. Provide short definitions of two words: sepal, and petal (be sure to cite your
sources even if you paraphrase):
Answer
A Sepal is one of the modified leaves comprising a calyx.
Reference: Sepal. In The Merriam-Webster.com Dictionary. Retrieved November 26,
2019, from https://www.merriam-webster.com/dictionary/sepal
Petal: one of the modified often brightly colored leaves of the corolla of a flower.
Reference: Petal. In The Merriam-Webster.com Dictionary. Retrieved November 26,
2019, from https://www.merriam-webster.com/dictionary/petal
2. There is a cumulative relative frequency table printed above for petal lengths (using
rounded values for petal length). Below the number 3 in that table is the number .35.
What does .35 represent? (multiple choice)
a. Three of the flowers had petal length of 0.35.
b. There were 0.35 observations that had petal length of 3 (after rounding the petal lengths).
c. Of all the flowers measured in this sample 35% had a petal length of 3 (after rounding the
petal lengths).
d. Of all the flowers measured in this sample 35% had a petal length of 3 or less (after
rounding the petal lengths). - Answer
e. A study of all flowers on the planet would show that about 35% had petal lengths of 3 or less
(after rounding the petal lengths).
3. Using only the cumulative relative frequency table printed above combined with some
simple paper-and-pencil calculations, which petal length occurs most frequently?
In order to BETTER answer this, I just pushed the relative frequency rounded to 0 decimals
back. You will find out that, if we just pick the accumulated relative frequency for 2 minus the
one for 1, we will get the frequency for 2, and so for, as shown below.
> rel.rfreq
x
1 2 3 4 5 6 7
0.16 0.17 0.02 0.23 0.23 0.16 0.03
pf3
pf4
pf5

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1. Sometimes it is difficult to understand data if you do not know what the numbers represent. Provide short definitions of two words: sepal, and petal (be sure to cite your sources even if you paraphrase): Answer  A Sepal is one of the modified leaves comprising a calyx. Reference: Sepal. In The Merriam-Webster.com Dictionary_. Retrieved November 26,_ 2019, from https://www.merriam-webster.com/dictionary/sepal  Petal: one of the modified often brightly colored leaves of the corolla of a flower. Reference: Petal. In The Merriam-Webster.com Dictionary_. Retrieved November 26,_ 2019, from https://www.merriam-webster.com/dictionary/petal 2. There is a cumulative relative frequency table printed above for petal lengths (using rounded values for petal length). Below the number 3 in that table is the number .35. What does .35 represent? (multiple choice) a. Three of the flowers had petal length of 0.35. b. There were 0.35 observations that had petal length of 3 (after rounding the petal lengths). c. Of all the flowers measured in this sample 35% had a petal length of 3 (after rounding the petal lengths). d. Of all the flowers measured in this sample 35% had a petal length of 3 or less (after rounding the petal lengths). - Answer e. A study of all flowers on the planet would show that about 35% had petal lengths of 3 or less (after rounding the petal lengths). 3. Using only the cumulative relative frequency table printed above combined with some simple paper-and-pencil calculations, which petal length occurs most frequently? In order to BETTER answer this, I just pushed the relative frequency rounded to 0 decimals back. You will find out that, if we just pick the accumulated relative frequency for 2 minus the one for 1, we will get the frequency for 2, and so for, as shown below.

rel.rfreq x 1 2 3 4 5 6 7 0.16 0.17 0.02 0.23 0.23 0.16 0.

[1] 0.

[1] 0.

[1] 0.

[1] 0.

[1] 0.

[1] 0.

This means that, with the cumulative frequency, we can calculate the relative frequency. And this shows clearly that the frequencies of 0.23 (4 and 5) occurs more frequently in our sample.

4. Describe how you determined your answer to the previous question (describe the calculations that you used). Do not show R code for this task--it will not be counted as an answer. So, if we are NOT SUPPOSED to use R to answer this, you should take the cumulative frequencies and subtract one from another to get a table just like this: 1 2 3 4 5 6 7 0.16 0.33 – 0. = 0.

And, yes, this CAN be done, just using a pencil. But, to be honest, I believe it was already DONE, in the exercise #2, just in order to calculate the relative frequencies table and the cumulative frequencies table.

[1] 5 5 5 5 5 5 5 5 4 5 5 5 5 4 6 6 5 5 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 5 5 6 5 4 5 5 4 4 5 5 5 5 5 5 5

[58] 5 7 5 5 6 6 6 6 7 6 6 6 6 6 6 6 6 6 7 7 7 6 6 6 6 6 6 5 6 7 6 6 6 6 6 6 5 6 6 6 6 5 6 6 6 7 6 6 8

[111] 6 6 6 8 8 6 7 6 8 6 7 7 6 6 6 7 7 8 6 6 6 8 6 6 6 7 7 7 6 7 7 7 6 6 6 6

Then, using the command: q.2 <- table(x.2)

freq. x. 4 5 6 7 8 5 47 68 24 6 So, the frequency of the value 7, as show in the above table (freq.2) is 24. This means that 24 observations have sepal with the length rounded to 7. Assuming that you read the flowers.csv file into an R object called flower.data, run the following R code (do not paste the ">” character into R). Note that we are not rounding the numbers here. Use the output for the next five tasks: table(flower.data$Sepal.Width) > plot(table(flower.data$Sepal.Width)) 2 2. 2

table(flower.data$Sepal.Width) plot(table(flower.data$Sepal.Width))

9. What is the sum of the first three frequencies in the frequency table for sepal width? Answer: 1 + 3 + 4 = 8 10. What does your answer to the previous question represent (in terms of sepal width and frequency and the percentage of all sepal measurements) Answer: Means that in 8 observation, the width of the sepal is less than or equal to 2.3. 11. What is the sum of the last three frequencies in the frequency table for sepal width? Answer: 1 + 1 + 1 = 3 12. How many flowers in the sample had sepal widths less than 4 (do NOT round the sepal width numbers for this, but you can round your final answer to 3 decimal places) Answer: 147