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The following were the grades obtained by 50 medical stds in their practicum in 1978. GRADE 1 2 3 4 5 6 7 8 9 FREQUENCY 4 8 7 12 4 9 3 1 2

The following were the grades obtained by 50 medical stds in their practicum in 1978.




FREQUENCY    GRADE

4                             1

8                             2

7                             3

12                           4

4                             5

9                             6

3                             7

1                             8

2                             9




 

a) What is the mode for this distribution/

b)What is the median grade?

c)find the mean grade.
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2 Answers

a) The mode is the grade that occurs most often. 4 occurs 12 times, more than any other grade. 4 is the mode.
 
b) The median grade is found by ordering all the grades from least to greatest, and then finding the midpoint between the 25th and 26th ordered grade. I will count up the frequencies until I find the 25th and 26th grade. 4+8=12, 12+7=19, 19+12=31. So both the 25th and 26th grade are 4; the midpoint between them is 4; the median is 4.
 
c) The mean is found by summing the products of the frequencies and the corresponding grades, and then dividing by the total of the frequencies. (4*1+8*2+7*3+12*4+4*5+9*6+3*7+1*8+2*9)/(4+8+7+12+4+9+3+1+2)=4.2
A) We simply look for the grade with the largest frequency, which would be 4 since it was obtained 12 times.
 
B) Because this sample has 50 observations, our median will be the average of the 25th and 26th largest. To see this, let's add in a third column to that table - cumulative frequency.
 
FREQUENCY      CUM. FREQ.       GRADE

4                             4                   1

8                            12                  2

7                            19                  3

12                          31                  4

4                            35                  5

9                            44                  6

3                            47                  7

1                            48                  8

2                            49                  9
 
We can see that the 25th and 26th observations are both 4 since both 25 and 26 fall between 31 and 17 (the cumulative frequencies of 4 and 3, respectively.) So our median is 4.
 
C) First of all, we find the sum of the grades obtained. This is just a matter of multiplying the grade by its frequency and adding those results together:
 
(1 * 4) + (2 * 8) + (3 * 7) + (4 * 12) + (5 * 4) + (6 * 9) + (7 * 3) + (8 * 1) + (9 * 2) = 210
 
We then find the average score in order to find our mean. That means our mean is 210/50 = 4.2.

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