2.5 Measures of the Center of the Data

Mean, median and mode computed from raw values and frequency tables, and why an extreme observation drags one of them and leaves another fixed.

Statistics, 2.5 Measures of the Center of the Data

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15 exercises

2.5 Exercise 1

Data indicating the number of months a patient with a specific disease lives after taking a new antibody drug are as follows (smallest to largest):
3, 4, 8, 8, 10, 11, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 21, 22, 22, 24, 24, 25, 26, 26, 27, 27, 29, 29, 31, 32, 33, 33, 34, 34, 35, 37, 40, 44, 44, 47
Calculate the mean and the median.

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2.5 Exercise 2

The following data show the number of months patients typically wait on a transplant list before getting surgery. The data are ordered from smallest to largest. Calculate the mean and median.

3, 4, 5, 7, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 17, 17, 18, 19, 19, 19, 21, 21, 22, 22, 23, 24, 24, 24, 24

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2.5 Exercise 3

Suppose that in a small town of 50 people, one person earns $5,000,000 per year and the other 49 each earn $30,000. Which is the better measure of the center: the mean or the median?

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2.5 Exercise 4

In a sample of 60 households, one house is worth $2,500,000. Half of the rest are worth $280,000, and all the others are worth $315,000. Which is the better measure of the center: the mean or the median?

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2.5 Exercise 5

50, 53, 59, 59, 63, 63, 72, 72, 72, 72, 72, 76, 78, 81, 83, 84, 84, 84, 90, 93

Find the mode.

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2.5 Exercise 6

The number of books checked out from the library by 25 students are as follows:

0, 0, 0, 1, 2, 3, 3, 4, 4, 5, 5, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12
Find the mode.

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2.5 Exercise 7

Five credit scores are 680, 680, 700, 720, 720. The data set is bimodal because the scores 680 and 720 each occur twice. Consider the annual earnings of workers at a factory. The mode is $25,000 and occurs 150 times out of 301. The median is $50,000, and the mean is $47,500. What would be the best measure of the center?

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2.5 Exercise 8

A frequency table displaying Professor Blount’s last statistic test is shown. Find the best estimate of the class mean.

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2.5 Exercise 9

Maris conducted a study on the effect that playing video games has on memory recall. As part of her study, she compiled the following data:

What is the best estimate for the mean number of hours spent playing video games?

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2.5 Exercise 11

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16, 17, 19, 20, 20, 21, 23, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 29, 30, 32, 33, 33, 34, 35, 37, 39, 40

Calculate the mean.

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2.5 Exercise 13

Identify the mode.

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2.5 Exercise 15

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars, 19 generally sell four cars, 12 generally sell five cars, nine generally sell six cars, and 11 generally sell seven cars. Calculate the following.

median = _______…

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2.5 Exercise 18

the table gives the percentage of children under age five have been diagnosed with a medical condition. What is the best estimate for the mean percentage of children with the condition?

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2.5 Exercise 20

What is the IQR?

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2.5 Exercise 22

Is this a sample or the entire population?

sample
entire population
neither

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