The value of one score in a distribution is changed from X = 20 to X = 30. Which measure(s) of central tendency is (are) certain to change?

Answer:

Mean

Step-by-step explanation:

The three basic measures of central tendencies are mean, median and mode.

Mean can be described as the average value of a set of numbers or scores in a distribution.

One of the ways the mean can be calculated is by dividing the sum of the scores in a distribution by the number of scores in the distribution. This can be represented mathematically as follows:

Mean = Sum of the scores in a distribution / Number of scores in the distribution ........ (1)

Median is the middle number when the scores in a distribution is arranged in ascending or descending order.

Mode is the most frequent number or score in a distribution.

Out of the three basic measures of central tendencies only the mean will certainly change when there is a change in one of the scores. This is because, we can still have the same score as the most frequent and the same number as the median but the mean will change.

For example, we can prove that the mean will certainly change if we assume that the sum of the scores in a distribution is 200 and number of scores in the distribution is 10, wee can substitute this into equation (1) and have:

Mean = 200 / 10 = 20

Now, as given in the question, if the value of one score in the distribution is changed from X = 20 to X = 30. We can obtain the difference as follows:

Difference in score = 30 - 20 = 10

The new mean can be calculated as follows:

New mean = (200 + Diffrence in score) / 20 = (200 + 10) / 20 = 210 / 20 = 21

Therefore, the mean changed by 1 from 20 to 21. This therefore proves that the mean will certainly change.

Of the measures of central tendency, the measure which will certainly change is the mean.

Measures of central tendency include mean, median and mode of a distribution.

The mean refers to the average, hence, the a change in one value in the distribution would certainly change the mean of the distribution.

The mode refers to the highest occurring value in the distribution.

Median denotes the number at the middle of a distribution once it is arranged in order of magnitude.

For instance :

The mean = (2 + 2 + 10 + 15 + 20) / 5 = 49/5 = 9.8

Mode = 2 (highest occuring)

Median = 10 (middle value)

If X = 20 is changed to X = 30

The mean = (2 + 2 + 10 + 15 + 30) = 59/5 = 11.8

Mode = 2 (highest occuring)

Median = 10 (middle value)

Therefore, the measure which would certainly change is the mean.

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