Question

Consider the following sample set of scores. Assume these scores are from a discrete distribution. 21 29 32 38 38 45 50 64 72 100 For the given data, the mean is ___ , the median is , and the mode is . Suppose the score 21 in the data is mistakenly recorded as 2 instead of 21. For the sample with this error, the mean is , the median is , and the mode is __ . The mean __ , the median ___ , and the mode ___ . Suppose the score 21 in the original sample is inadvertently removed from the sample. For the sample with this score removed, the mean is ___ , the median is __ , and the mode is __ . The mean ___ , the median __, and the mode ___

Answer 1

Answer:

Original data: 21 29 32 38 38 45 50 64 72 100

$\bar X = \frac{21+29+32+38+38+45+50+64+72+100}{10}=48.9$

Mode =38.

$Median = \frac{38+45}{2}=41.5$

Change 1: 2 29 32 38 38 45 50 64 72 100

$\bar X = \frac{2+29+32+38+38+45+50+64+72+100}{10}=47$

Mode =38.

$Median = \frac{38+45}{2}=41.5$

Change 2: 29 32 38 38 45 50 64 72 100

$\bar X = \frac{29+32+38+38+45+50+64+72+100}{9}=52$

Mode =38.

$Median = 45$

Step-by-step explanation:

Original data: 21 29 32 38 38 45 50 64 72 100

The mean is calculated with the following formula:

$\bar X = \frac{\sum_{i=1}^{10} X_i}{10}$

And if we replace we got:

$\bar X = \frac{21+29+32+38+38+45+50+64+72+100}{10}=48.9$

The mode is the most repeated value in the sample and on this case is Mode =38.

Since we have an even number of points the median is calculated as the average between the observations 5 and 6 from the dataset ordered.

$Median = \frac{38+45}{2}=41.5$

Change 1: 2 29 32 38 38 45 50 64 72 100

The mean is calculated with the following formula:

$\bar X = \frac{\sum_{i=1}^{10} X_i}{10}$

And if we replace we got:

$\bar X = \frac{2+29+32+38+38+45+50+64+72+100}{10}=47$

The mode is the most repeated value in the sample and on this case is Mode =38.

Since we have an even number of points the median is calculated as the average between the observations 5 and 6 from the dataset ordered.

$Median = \frac{38+45}{2}=41.5$

Change 2: 29 32 38 38 45 50 64 72 100

Now the sample size is 9 instead of 10

The mean is calculated with the following formula:

$\bar X = \frac{\sum_{i=1}^{9} X_i}{9}$

And if we replace we got:

$\bar X = \frac{29+32+38+38+45+50+64+72+100}{9}=52$

The mode is the most repeated value in the sample and on this case is Mode =38.

Since we have odd number of points the median is calculated from the 5 position of the dataset ordered.

$Median = 45$