Twenty-three students wrote a statistics examination having a maximum of 50 marks. The mark distribution is given in the following stem-and-leaf diagram:
0 9
1 25
2 01335889
3 001369
4 02248
5 0
Q1 is equal to:
a) 15
b) 21
c) 23
d) None of the above
THE ANSWER IS: C
Please Explain why. Greatly appreciated.
To find Q1 (the first quartile), we need to determine the mark below which 25% of the students scored. Here's how we can solve it step by step:
1. Start by rearranging the stem-and-leaf diagram in ascending order:
0 9
1 25
2 01335889
3 001369
4 02248
5 0
2. Combine the stems and leaves to form the actual marks:
0, 9, 1, 1, 1, 2, 0, 3, 3, 5, 8, 9, 2, 0, 1, 3, 5, 9, 3, 6, 9, 4, 2, 2, 4, 8
3. Calculate the total number of marks:
N = 23 (since there are 23 students)
4. Determine the position of Q1:
Q1 = (1/4) * (N + 1) = (1/4) * (23 + 1) = (1/4) * 24 = 6
5. Find the mark at the 6th position:
In the rearranged list, the 6th mark is 3.
Therefore, Q1 is equal to 3, and the correct answer is option c) 23.