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Elementary Statistics Discussion Assignment

Dr. Tomas Kovarik: Statistics Homework 2(Descriptive Statistics – Univariate) 8

STATISTICS: HOMEWORK 2 (Descriptive Statistics

1) For the data: 43, 60, 15, 25, 16, 30, 44, 400, 70 , 90, 40, 10, 0, 66, 70 calculate

a) Mean, Median and Mode

b) Which measure of center is better: Mean or Median? Explain

c) Calculate Quartiles

d) Calculate the Range and Interquartile Range

e) Use the IQR test to determine if there are any outliers

f) Construct the modified box plot

g) Calculate percentile

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65

P

and decile

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8

D

2) You are sitting by the road and record the color of each passing car. After an hour you see 10 red cars, 15 blue cars, 7 white cars, 8 yellow cars. Costruct a distribution (frequency) table and the Bar Chart based on the above categories

3) Consider the following frequency table:

Data

Frequency

Relative frequency

Cumulative relative frequency

10

2

14

3

15

5

16

4

20

1

25

4

30

7

a) Fill in the columns

b) Construct a Relative Frequency Bar Chart

c) Calculate the Mean and Median and the Mode

d) Calculate the sample standard deviation (as if the data was a random sample of a population)

e) Calculate the 30th Percentile

f) Calculate the sample z – score which corresponds to the raw score of x = 10

4) Consider the following data (Grades on a Statistics Test)

0, 45,60,30,50,75,75,90,25,50,30,20,80,95,95,90,90,100,55,60,65,70,70,70,70,70,85,60

The letter grades are:

A….90 and above

B+….86 – 89

B…. 80 – 85

C+…76 – 79

C…..70 – 75

D….60 – 69

F….below 50

a) Construct a Frequency Table based on the classes (grades).

b) Construct a Relative Frequency Histogram based on the classes and comment on the shape

c) Calculate the Population Standard Deviation of the data and the population z – score corresponding to the raw score x = 50

d) What is the (exact) proportion of students in our sample, who fall within 2 standard deviation of the mean? And how does that compare to the Empirical Rule ?

e) Construct the Stem and Leaf Diagram

5) Professor gives an exam and the class average is 75% with standard deviation of 5

Your grade is 85. Calculate your z – score and interpret it in the light of the Empirical Rule. What do you need to assume about the grades in order to use the Empirical Rule?

6) Your z – score in a class in which the average is 80 with standard deviation of 10 is z = 1.6. What is your real test score?

7) Your Statistics teacher refused to give you your real grade, but told you that your z – score was 2.5. Using Chebychev’s and Empirical Rule, how happy or unhappy are you about the information?

8) Suppose that the distribution shape of grades is left skewed. How does the mean compare to the median? How about if the distribution is right skewed? How about if it is symmetric? Check in on this example: 10, 25, 25, 30, 30, 30, 40, 40, 40, 40, 40

(Namely, draw the histogram and find out its shape and then compare the mean and the median)

9) Consider the Stem and Leaf Diagram:

4 05

5 05

6 05

7 0000555

8 0005

9 0555

10 0

a) Construct a frequency table based on class width 10

b) Construct frequency histogram based on the above classes

c) Calculate the quartiles

d) Construct boxplot

e) Calculate the Mean, Median and Mode

f) Calculate the Sample Variance and Standard Deviation

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