1. The data below shows the scores of students in a Mathematics test: 2, 5, 5, 4, 2, 3, 5, 3, 4, 5, 5, 2, 3, 1, 4, 1, 3, 3, 2, 5, 3, 2, 3, 4, 2, 3, 3, 5, 3, 1. Use the information to answer questions below.
(a) Prepare a frequency table for the data;
(b) If a pie chart of the information is drawn, calculate the sectoral angle representing each score.
(c) What is the probability that a student chosen at random will score 4 and above?
Answer (2)
(a) Frequency Table
To create a frequency table, we first list all the unique scores and then count how many times each score appears in the data set.
ScoreFrequency13263844555.51
(b) Sectoral Angles
To calculate the sectoral angles for a pie chart, we first find the total number of scores and then use the formula:
Sectoral Angle = ( Total Frequency Frequency of the Score ) × 360
The total number of scores is 27.
For 1 : ( 27 3 ) × 360 = 4 0 ∘
For 2 : ( 27 6 ) × 360 = 8 0 ∘
For 3 : ( 27 8 ) × 360 = 106.6 7 ∘
For 4 : ( 27 4 ) × 360 = 53.3 3 ∘
For 5 : ( 27 5 ) × 360 = 66.6 7 ∘
For 5.5 : ( 27 1 ) × 360 = 13.3 3 ∘
(c) Probability of Scoring 4 and Above
To find the probability that a student chosen at random will score 4 or above, we add the frequencies of scores 4, 5, and 5.5, then divide by the total number of scores.
Scores 4 and above: 4 + 5 + 1 = 10
Total scores: 27
Probability = 27 10 ≈ 0.370
A frequency table was created showing the scores and their counts. The sectoral angles for a pie chart were calculated, with angles corresponding to each score. Finally, the probability of selecting a student scoring 4 or above was determined to be approximately 0.370.
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