Question

Consider the following grades on a test: 98, 51, 94, 67, 94, 73, 75, 89, 22, 99, 84, 89, 87, 93, 81, 92, 71, 61, 10     The mean is 75. Create a stem and leaf display of the data and then answer the following question:

True or False:

a)    Most students made C’s.
b)    Most students made right around the mean of 75.
c)    There was a balanced amount of A’s, B’s, C’s, D’s, and F’s.
d)    Half of the grades were below 75 and half above

Answer 1

For the given data set:

98, 51, 94, 67, 94, 73, 75, 89, 22, 99, 84, 89, 87, 93, 81, 92, 71, 61, 10

The mean is caluclated as:

Mean = (98 + 51 + 94 + 67 + 94 + 73 + 75 + 89 + 22 + 99 + 84 + 89 + 87 + 93 + 81 + 92 + 71 + 61 + 10)/19
= 1430/19
Mean = 75.2632

Now the stem and leaf plo which is reperesented to show the distribution of the data set on the basis of each values place value.

In a stem-leaf plot, the stem is the tens place digit of the values and the ones is the Leaf values, the plot is plotted below:

Stem Leaf 10 22 5 1 6 17 7 135 8 14799 9 23 4 4 8 9

From the Plot shown above

a)    Most students made C’s. - False if the 'C' grade is given to those who score less than 70, because most in the dataset are above the 70s.

b)    Most students made right around the mean of 75.- False, As we can see that the maximum of data values are above 75.
c)    There was a balanced amount of A’s, B’s, C’s, D’s, and F’s. -False because again most of the Data values are above the '70s and no distributed evenly throughout the distribution.
d)    Half of the grades were below 75 and a half above- False once again most of the data set are above 70 so, we cannot say that half is below 75 and half is above 75.

Note: Please see that there is no details given about the grading system, so, first compare them then submit the anser.

Feel free to ask if problem persists.