Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Question

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Answer 1

Question

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Conclusion

The mean is most easily distorted by very large or very small scores.

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Answer 2

Question

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Conclusion

The mean is most easily distorted by very large or very small scores.

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Answer 3

Question

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Conclusion

The mean is most easily distorted by very large or very small scores.

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Answer 4

Question

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Conclusion

The mean is most easily distorted by very large or very small scores.

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Answer 5

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Conclusion

The mean is most easily distorted by very large or very small scores.

Answer 6

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Conclusion

The mean is most easily distorted by very large or very small scores.

Answer 7

Chapter 3, Problem 1MM

Summary Introduction

Introduction: Measures of central tendency contribute to summarizing data. These involve the mode, the median, and the mean that represent the middle of the data distribution. The mode is the value that occurs most commonly in distribution, the median is the middle value, and mean is the average value of the observations.

Answer 8

Expert Solution & Answer

Answer to Problem 1MM

Correct answer: The mean is the measure of central tendency that is most easily distorted by few very large or very small scores. Therefore, option b. is correct.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Reason for the correct statement:

The mean value is obtained by summing the scores and dividing it with the number of scores. It involves every score in the distribution; thus, any change in the score value would alter the value of mean. If the distribution contains some extreme scores (such as very small or very large values), the mean would be easily displaced. In this case, the mean would not provide the central value.

Hence,option b. is correct.

Reasons for the incorrect statement:

Option a. is given as “the mode”. The mode is the most commonly occurring score in the distribution. Hence, it is a wrong answer.

Option c. is given as “the median”. It is the middle value when data is distributed in ascending or descending order. It requires scores from smallest largest values. Hence, it is a wrong answer.

Option d. is given as “they are all equally vulnerable to distortion from atypical scores”. All three measures of central tendency are equally distributed if there is symmetrical distribution. The mean denotes the average value, so it is most commonly distorted with extreme variations in the scores. Hence, option d. is incorrect.

Hence, options a., c., and d. are incorrect.

Answer 12

Conclusion

The mean is most easily distorted by very large or very small scores.

Answer 13

Ch. 3 - Prob. 1MM Ch. 3 - Prob. 2MM Ch. 3 - Prob. 3MM Ch. 3 - Prob. 4MM

Answer to Problem 1MM

Explanation of Solution

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Chapter 3 Solutions