Question

The number of credits being taken by a sample of 13​ full-time college students are listed below. Find the​ mean, median, and mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why.                            Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The mean is nothing. ​(Type an integer or decimal rounded to one decimal place as​ needed.) B. The data set does not have a mean. Does the mean represent the center of the​ data? A. The mean represents the center. B. The mean does not represent the center because it is not a data value. C. The mean does not represent the center because it is the smallest data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The median is nothing. ​(Type an integer or decimal rounded to one decimal place as​ needed.) B. The data set does not have a median. Does the median represent the center of the​ data?

Answer 1

Answer:

The data is missing in the question, below is the complete question:

The number of credits being taken by a sample of 13​ full-time college students are listed below. Find the​ mean, median, and mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why. 9    9    12    12    9    10    8    8    8    8    8    8    11    Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The mean is nothing . ​(Type an integer or decimal rounded to one decimal place as​ needed.) B. The data set does not have a mean. Does the mean represent the center of the​ data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is not a data value. D. The mean does not represent the center because it is the largest data value. E. The data set does not have a mean. Find the median. Select the correct choice below​ and, if​necessary, fill in the answer box to complete your choice. A. The median is nothing . ​(Type an integer or decimal rounded to one decimal place as​ needed.) B. The data set does not have a median. Does the median represent the center of the​ data? A. The median represents the center. B. The median does not represent the center because it is the largest data value. C. The median does not represent the center because it is not a data value. D. The median does not represent the center because it is the smallest data value. E. The data set does not have a median. Find the mode. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The​ mode(s) is/are nothing . ​(Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as​ needed.) B. The data set does not have a mode. Does​ (Do) the​ mode(s) represent the center of the​ data? A. The​ mode(s) represent(s) the center. B. The​ mode(s) does​ (do) not represent the center because it​ (they) is​ (are) not a data value. C. The​ mode(s) does​ (do) not represent the center because it​ (one) is the largest data value. D. The​ mode(s) does​ (do) not represent the center because it​(one) is the smallest data value. E. The data set does not have a mode.

Answer:

a.) mean = 9.23

ii) The mean represents the centre (A)

b) Median = 9

ii) The median represents the centre (A)

c) Mode = 8

ii)  The​ mode(s) does​ (do) not represent the center because it​(one) is the smallest data value. (D)

Step-by-step explanation:

Arranging the data in ascending order:

8 8 8 8 8 8 9 9 9 10 11 12 12

a) calculating for mean

$\bar x = \frac{sum\ of\ data}{number\ of\ data}\\ \bar x = \frac{8+8+8+8+8+8+9+9+9+10+11+12+12}{13} \\\bar x =\frac{120}{13} \\\bar x = 9.23$

ii) does the mean represent the centre of the data?

The measure of central tendency/location is a statistical tool used to accurately depict values that are at the central location of the data set

Yes, the mean represents the centre of the data, because there are no outliers in the data set. Outliers are unusual values compared to the rest of the values in the dataset.

b) calculating the median (M)

$M =( \frac{n\ +\ 1}{2})th\ term\\ \\where:\\n = number\ of\ data\ in\ the\ dataset = 13\\\\\therefore M = \frac{13+1}{2}\\ M = \frac{14}{2} \\M= 7th\ term$

The 7th term after arranging in ascending or descening order, is the median term

8 8 8 8 8 8 9 9 9 10 11 12 12

∴ Median = 9

ii) Yes, the Median represents the center of the data, because it litterally tells the data at the middle of the distribution  

c) The mode is the data with the highest number of occurrence in the dataset (highest frequency);  8 8 8 8 8 8 9 9 9 10 11 12 12

The data with the highest number of occurrence is 8, which occurred 6 times.

Mode = 8

ii) The mode does not represent the centre of the data because it is the smallest value in the dataset, hence it doesn't tell the value that is the middle term.