We are asked to find the value of f in the table. Since we are told that the mean of the scores is 3.5, we can use it to find f. Let's begin by recalling the definition of mean.
Mean=Sum of the data values/Number of values
Since we are given a frequency table, we have to multiply each score by its frequency in order to find the sum of the data values. Let's find this sum and simplify!
1(1)+3(2)+f*3+ 12(4) + 3(5) ⇓
Sum of the data values= 3f+70
The total number of values is the sum of the frequencies of each score.
1+3+f+12+3 ⇓ Number of values = f+19
We will now use the definition of mean to write and solve an equation for f.
We found that f=7. This means that 7 students scored 3 in the exam.
b We found in Part A that f=7. Let's use this to rewrite the given frequency table!
Score
1
2
3
4
5
Frequency
1
3
7
12
3
The mode is the value or values that appear most often in a data set. Since we are given a frequency table, the mode is the value with the highest frequency.
Score
1
2
3
4
5
Frequency
1
3
7
12
3
Therefore, the mode of the scores is 4.
c When the data is arranged in numerical order the median is the middle value — or the mean of the two middle values — of the set. Let's use our frequency table from Part B and list all the scores.
1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5
Since we have 26 values, which is an even number, the median is the mean of the two middle values.
Median=4+ 4/2=4
