2020-introduction to applied statistics(stat213)-class 4 notes PDF

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Class problem sets...

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Class #4

Measures of Spread

1. Here is a set of data describing the number of laps swum by Brittany in 30 days. Stem

Leaf

1L

0

1H

89

2L

0122444

2H

5566677778888899

3L

112

3H

9

Where 1 | 8 means 18 laps were swum. a) Find the mean of the data

b) Find the median of the data

c) What feature of the data indicated the two measures of center might be reasonably close in value?

2. . a) How many data values will be in each of the lower and the upper half of the data ?

b) Determine the highest number in the lower half of the data.

c) Determine the lowest number in the upper half of the data.

3. a) Fill in these 5 numbers:

the lowest value in the data set (minimum)

the median of the the median of the lower half of the data data

the median of the the highest value in upper half of the data the data (maximum)

These 5 numbers constitute the 5 number summary. They are denoted as: min

Q1

M

Q3

max

4. Here are 3 classes of AP calculus scores from a semester at another school taught by the same teacher. a) Give the 5 number summary (approximately) for each.

b) Discuss similarities or differences between the classes. 5. The Interquartile Range, or IQR is the width of the box—the boundaries of the central 50% of the data. a) Which of the classes have the most similar IQR?

b) Find the (approximate IQR) for the class which is the “odd one out”. c) Which class had the most consistent scores? That is, which class appeared to have the least amount of variation?

6. Outliers: There are several ways to determine if some data point is an outlier. a) For Class D above, Determine the IQR then multiply it by 1.5 We will call this the “fence measurer”. b) Subtract this number from the first quartile. This number is the “lower fence”. c) Add the “fence measurer” to the third quartile. This number is the “upper fence”. d) Are there any numbers beyond the fences?

7. 7 people are randomly polled and they are asked how many eggs they eat in a week. The dataset of x values is: 0

4

6

8

10

10

11

Unit: eggs

a) The mean is 7. Find the deviation from the mean for each value. Deviation= x− ¯x b) What must be true of a data value in order for the deviation from the mean to be negative? positive?

c) Add the deviations.

d) Add the squares of the deviations. What unit is this sum measured in?

e) The (sample) variance of a data set is given by

∑ ( x− ¯x)2 n−1

and is denoted

s

2

. Compute it.

f) The (sample) standard deviation is the square root of the variance and is denoted

s . Compute it.

8. Looking back at the class scores data. Which data might you guess has the lowest standard deviation?

9.

Look at the following data sets:

sample data set 1:

2

2

2

2

2

2

2

2

sample data set 2:

0

0

0

0

4

4

4

4

sample data set 2:

0

0

1

1

2

4

4

4

The mean for each is 2.

Find the sample variance and sample standard deviation for each.

10. Look at this “data”.

3

5

5

7

7

9

11

Which standard deviation below makes the least sense for this? 1

11.

12

3.5

14 Which might be in the right ballpark?

-2

A test was given .

The possible scores were between 0 and 100. The average was a 90. The standard deviation of scores was a 25. How is this possible?

12. Here are two distributions given as ahistogram and a box plot. Discuss how you’d know which was with which:...