Theory question 112
StatisticsThe marks obtained by 40 students in an examination are as follows:
29 52 37 79 63 48 65 46 54 32 51 66 74 24 35 61 58 39 49 53
45 58 56 38 59 28 50 49 67 56 37 45 79 68 43 66 26 47 55 71
(a) Construct a grouped frequency distribution table using the class interval 20 − 29, 30 − 39, 40 − 49 …
(b) Using an assumed mean of 54.5, calculate, correct to the nearest whole number, the: (i) Mean mark
(ii) Standard deviation of the distribution
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(a) 20–29: 4; 30–39: 6; 40–49: 8; 50–59: 11; 60–69: 7; 70–79: 4 (total 40).
(b) Class marks 24.5 … 74.5; d = x − 54.5 = −30, −20, −10, 0, 10, 20.
Σfd = −120 − 120 − 80 + 0 + 70 + 80 = −170; Σfd² = 3600 + 2400 + 800 + 0 + 700 + 1600 = 9100.
(i) Mean = 54.5 + (−170/40) = 50.25 ≈ 50.
(ii) SD = √(9100/40 − (−4.25)²) = √209.44 ≈ 14.5, i.e. 14 to the nearest whole number.
Tally carefully and check the frequencies add up to 40.