Why is it necessary to have more than one method for measuring central tendency?

Question

Why is it necessary to have more than one method for measuring central tendency? Find the mean, median, and mode for the following sample of scores: 5 4 5 2 7 1 3 5 Find the mean, median, and mode for the following sample of scores: 3 6 7 3 9 8 3 7 5 Find the mean, median, and mode for the scores in the following frequency distribution table: Find the mean, median, and mode for the scores in the following frequency distribution table: For die following sample: a. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. b. Assume that the scores are measurements of a discrete variable and find the median. Scores: 1 2 3 3 3 4 A population of N = 15 scores has sigma X = 120. What is the population mean? A sample of n = 8 scores has a mean of M = 12. What is the value of sigma X for this sample? A population with a mean of mu = 8 has sigma X = 40. How many scores are in the population? A sample of n = 7 scores has a mean of M = 9. If one new person with a score of X = 1 is added to the sample, what is the value for the new mean? A sample of n = 6 scores has a mean of M = 13. If one person with a score of X = 3 is removed from the sample, what it the value for the new mean? A sample of n = 15 scores has a mean of M = 6. One person with a score of X = 22 is added to the sample. What is the value for the new sample mean? A sample of n = 10 scores has a mean of M = 9. One person with a score of X = 0 is removed from the sample. What is the value for the new sample mean? A population of N = 15 scores has a mean of mu = 8. One score in the population is changed from X = 20 to X = 5. What is the value for the new population mean? A sample of n = 7 scores has a mean of .M = 16. One score in the sample is changed from X = 6 to X = 20. What is the value for the new sample mean? A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found to be M = 6. What is the value of the new score? A population of N = 8 scores has a mean of mu =16. After one score is removed from the population, the new mean is found to be mu = 15. What is the value of the score that was removed? A sample of n = 9 scores has a mean of M = 13. After one score is added to the sample, the mean is found to be M = 12. What is the value of the score that was added? A sample of n = 9 scores has a mean of. M = 20. One of the scores is changed and the new mean is found to be M = 22. If the changed score was originally X = 7, what is its new value? One sample of n = 12 scores has a mean of M = 7 and a second sample of n = 8 scores has a mean of M =12. If the two samples are combined, what is the mean for the combined sample? One sample has a mean of M = 8 and a second sample has a mean of .M =16 The two samples are combined into a single set of scores. a. What is the mean for the combined set if both of the original samples have n = 4 scores? b. What is the mean for the combined set if the first sample has n = 3 and the second sample has n = 5?

Explanation / Answer

As per the chegg policy, we are advised to do one question at a time. I am attempting the 2nd one.

2. On arranging the given data into ascending order,

1 2 3 4 5 5 5 7

So,

Mean = (Sum of observations)/(Number of observations)

= (1 + 2 + 3 + 4 + 5 + 5 + 5 + 7)/8

= 32/8

= 4

Number of terms = 8

So,

Median = Average of 4th and 5th term = (4 + 5)/2 = 4.5

Mode = Most occured value = 5

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