Theory question 113
Data PresentationMarks: 10, 20, 30, 40, 50, 60, 70, 80, 90
Frequency: 1, 1, x, 5, y, 1, 4, 3, 1
The frequency table shows the marks distribution of a class of 30 students in an examination. The mean mark of the distribution is 52. (a) Find the values of x and y. (b) Construct a group frequency distribution table starting with a lower class limit of 1 and a class interval of 10. (c) Draw a histogram for the distribution. (d) Use the histogram to estimate the mode.
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(a) 16 + x + y = 30 → x + y = 14
Σfx = 900 + 30x + 50y = 52 × 30 = 1560 → 3x + 5y = 66
Solving: y = 12, x = 2
(b) Classes 1–10, 11–20, …, 81–90 with frequencies 1, 1, 2, 5, 12, 1, 4, 3, 1 (class boundaries 0.5–10.5, …, 80.5–90.5)
(c) Bars on the class boundaries with heights equal to the frequencies.
(d) Modal class 40.5–50.5: draw the crossing lines in the tallest bar; mode ≈ 40.5 + 7/(7 + 11) × 10 ≈ 44.4
In (d) join the top corners of the tallest bar to the neighbouring bars and read where the lines cross.