Stat Lab 2.2 and 2.3 PDF

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Stat lab 2.2 and 2.3 - use for reference...

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LAB 2.2 &23 Statistics 200: Lab Activity for Sections 2.2 and 2.3. Measures of center and spread for one quantitative variable - Learning objectives:  Use a dotplot or histogram to describe the shape of a distribution  Find the mean and the median for a set of data values, with appropriate notation  Explain how outliers and skewness affect the values for the mean and median  Use technology to compute summary statistics for a quantitative variable  Recognize the uses and meaning of the standard deviation  Compute and interpret a z-score  Interpret a five number summary or percentiles  Use the range, the interquartile range, and the standard deviation as measures of spread  Describe the advantages and disadvantages of the different measures of center and spread Activity 0: This lab uses Minitab. Remember to access the guide on Canvas. Activity 1: What percent of students who start college at a 4-year college or university graduate from that college within 6 years? The data values below are the 6-year graduation rate, rounded to the nearest percent, for the 14 Big 10 universities. (https://www.thoughtco.com/comparison-of-the-big-ten-universities-786967)

A Comparison of the Big Ten Universities University Rate University Rate Illinois 85 Nebraska 67 Indiana 76 Northwestern 94 Iowa 72 Ohio State 84 Maryland 87 Penn State 86 Michigan 91 Purdue 77 Michigan State 78 Rutgers 80 Minnesota 78 Wisconsin 85 1. Using Minitab, enter this data and then find the following statistics: n = 14 Five Number Summary: Minimum Q1 67 76.75

Mean = 81.43 Median 82

Standard deviation = 7.37 Q3 86.25

Maximum 94

2. What is the IQR for this dataset? 9.5 What is the range? 27 3. Which interval of the data contains: the lowest 25%? the upper 75%? the middle 50%? the upper 50%?

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Q1 Q1-max Q1-q3 Q3-max

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LAB 2.2 &23

4. What is the Z-score for the observation 90? Complete the interpretation below for this value: The observation 90 is 1.16 standard deviations above the sample mean of 81.43.

5. What is the Z-score for the observation 70? Complete the interpretation below for this value: The observation 70 is 1.55 standard deviations below the sample mean of 81.43.

6. What if you made a mistake (typo) when entering the data. Typo 1 Sample: With Northwestern, you entered 940 instead of 94. Typo 2 Sample: With Nebraska, you entered 7 instead of 67. With each Typo, when considering the following statistics, decide whether they would stay roughly the same, become much larger, or become much smaller, when compared to the original sample. Statistic Mean Median IQR Range Standard Deviation

Typo 1 Sample larger same same larger larger

Typo 2 Sample smaller same same larger larger

When comparing the mean to the median, which shape would go with each sample? Sample Shape Original Sample symmetric Typo 1 Sample right skewed Typo 2 Sample left skewed You should be able to decide without Minitab, but if you’d like to check your work you can intentionally make the data entry mistake and then compute the statistics. Activity 2: Histograms, dotplots, and shape. Open the dataset ‘StudentSurvey’ (available on Canvas) in Minitab. Recall that these data are student responses to a survey. Consider the variables ‘TV’ (hours per week), ‘SAT’ (scores on SAT exam), ‘MathSAT’ (scores on the math section of the SAT exam), and ‘Exercise’ (hours spent exercising per week). 1. Without plotting these variables, what is your intuition about their shapes? (symmetric, bellshaped, right-skewed, left-skewed) Shape intuition

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TV Left skewed

SAT Bell shaped

MathSAT Bell shaped

Exercise Right skewed

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LAB 2.2 &23

2. Now create a dotplot for each of the variables separately. 3. Consider the dotplot for ‘TV’, what does a single dot represent? Hours a person watched tv 4. Now that you have dotplots for each of the variables, complete the table below. For shape, choose between symmetric, right-skewed, and left-skewed. For mean ___ median: decide if the mean is about equal to, less than, or greater than the median. For 95% rule, decide whether or not it would be appropriate to apply the 95% rule. Shape Mean ___ Median

TV right greater

SAT sym equal

MathSAT sym equal

Exercise right greater

95% rule

no

yes

yes

no

5. For the variable SAT, use the 95% rule to complete the sentence below: Roughly 95% of the SAT scores are between 960 and 1440. Activity 3: The graph below displays four samples, each based on n = 20, with a min of 1 and a max 10.

Four Dotplots (n = 20)

Star Oval

Circle Square

1

3

5

7 Data

9

11

13

Rank the samples from smallest to largest, when considering the value for the standard deviation.

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LAB 2.2 &23 Circle, oval, square, star

Activity 4: Words with Friends points for your name 1.

Sign your name in the space below using your usual signature (first and last name)

2.

Print the letters in your signature (even the illegible parts!) in the boxes below.

g 3 3.

e o r g i a m a l o 1 1 1 3 1 1 4 1 2 1 Count the number of letters in your signature (ignoring blanks and punctuation).

Number of letters in my signature: 11 4.

Using the table below, determine the Words with Friends point value for each of the letters in your signature. Write the values beneath each letter in the printed version of your signature above.

a b c d e f g h i j k l m n o p q r s t u v w x y z 1 4 4 2 1 4 3 3 1 10 5 2 4 2 1 4 10 1 1 1 2 5 4 8 3 10 5. Add the values of the Words with Friends points for the letters in your signature. Points value of my signature 20

6. Enter your answers to questions 3 and 5 through Canvas (see submodule for this section).

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