Statistics I
14 Grade 10 Core Mathematics questions on Statistics I, with worked marking schemes. 14 questions are available on this topic in full.
Question 1
1 markA dairy farmer in Nyandarua recorded the milk, in litres, collected on five consecutive mornings as 18, 22, 20, 25 and 20. Determine the mean daily collection.
A. 20 litres
B. 21 litres
C. 7 litres
D. 26.25 litres
(1 mark)
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1 markIn a Grade 10 mathematics quiz marked out of 20, six learners scored 12, 15, 11, 18, 14 and 20. Determine the median score.
A. 14.5
B. 14
C. 15.5
D. 15
(1 mark)
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1 markA Grade 10 class recorded the amount of pocket money each learner brought to school. One learner brought an amount far larger than that of every other learner. Which measure of central tendency is most affected by that single amount?
A. The mode
B. The mean
C. The range
D. The median
(1 mark)
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5 marksA learner standing at the school gate counted the matatus passing each day for ten days and recorded 14, 9, 12, 14, 20, 9, 14, 11, 16 and 13.
(a) Determine the range.
(b) State the mode.
(c) Determine the median.
(d) Explain why the range alone is a poor description of this set of data.
(5 marks)
Marking scheme
(a) Range = 20 - 9 = 11 matatus (1 mark). (b) Mode = 14 matatus, as it occurs three times (1 mark). (c) Ordered values: 9, 9, 11, 12, 13, 14, 14, 14, 16, 20; the two middle values are 13 and 14 (1 mark); median = (13 + 14) / 2 = 13.5 matatus (1 mark). (d) The range uses only the largest and smallest values and ignores the other eight readings, so it says nothing about how the counts are distributed and is distorted by any single unusual day (1 mark).
Question 5
1 markThe heights of maize plants in a school garden were measured to the nearest centimetre and grouped into classes whose class boundaries are 99.5-109.5, 109.5-119.5, 119.5-129.5 and 129.5-139.5. State the class width.
A. 10.5 cm
B. 10 cm
C. 9 cm
D. 19 cm
(1 mark)
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3 marksThe masses, in kilogrammes, of eight bunches of bananas delivered to a Kisii market were 12, 15, 11, 15, 18, 14, 24 and 15. Determine the mean, the median and the mode of the masses.
(3 marks)
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1 markBags of Irish potatoes at a store were weighed and grouped as follows: 40-44 kg (3 bags), 45-49 kg (7 bags), 50-54 kg (12 bags), 55-59 kg (9 bags) and 60-64 kg (4 bags). State the class boundaries of the modal class.
A. 54.5 kg and 59.5 kg
B. 44.5 kg and 49.5 kg
C. 50 kg and 54 kg
D. 49.5 kg and 54.5 kg
(1 mark)
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4 marksThe masses, in kilogrammes, of 20 bags of beans delivered to a Kitui store were grouped as: 20-29 (4 bags), 30-39 (6 bags), 40-49 (7 bags) and 50-59 (3 bags). Calculate an estimate of the mean mass of a bag.
(4 marks)
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1 markThe number of mangoes harvested from each of 10 trees in a Machakos orchard was grouped as 10-14 mangoes (2 trees), 15-19 mangoes (5 trees) and 20-24 mangoes (3 trees). Estimate the mean number of mangoes per tree.
A. 17.0
B. 17.5
C. 58.3
D. 15.0
(1 mark)
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3 marksExplain why the mean calculated from a grouped frequency distribution is only an estimate of the true mean of the original data.
(3 marks)
Marking scheme
Award 1 mark each, to a maximum of 3: (i) once data is grouped the individual values are lost, so the exact total cannot be recovered; (ii) every value in a class is assumed to lie at the class midpoint, which is rarely true; (iii) the actual values are usually spread unevenly within a class, so the assumed midpoint over- or under-states them; (iv) therefore the calculated value is an approximation and will normally differ from the mean of the raw data.
Question 11
3 marksOutline three steps a learner should follow when constructing a frequency distribution table from a list of raw measurements.
(3 marks)
Marking scheme
Award 1 mark each, to a maximum of 3: (i) find the range of the raw data and use it to decide on a suitable number of classes and a common class width; (ii) write down the classes so that they are of equal width, do not overlap, and together cover every value in the data; (iii) go through the raw data once, placing a tally mark against the class in which each value falls; (iv) count the tallies in each class and record the totals as the frequencies, then check that the frequencies add up to the number of items in the data.
Question 12
2 marksA shopkeeper says the average number of loaves of bread she sells per day is 40, yet on most days she sells about 25 loaves. Suggest a reason for this difference and state which measure of central tendency would better describe a typical day.
(2 marks)
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1 markIn a Grade 10 class of 40 learners, the number of younger brothers and sisters each learner has was recorded as: 0 (6 learners), 1 (14 learners), 2 (10 learners), 3 (7 learners) and 4 (3 learners). Determine the median number of younger brothers and sisters.
A. 1.5
B. 1.7
C. 2
D. 1
(1 mark)
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4 marksDistinguish between discrete data and continuous data, giving one example of each drawn from a Kenyan farm.
(4 marks)
Marking scheme
Discrete data: data obtained by counting, taking only exact separate (usually whole number) values (1 mark). Example: the number of goats in a herd, or the number of maize plants in a row (1 mark). Continuous data: data obtained by measuring, which can take any value within a range and depends on the accuracy of the instrument (1 mark). Example: the volume of milk, in litres, obtained from one cow, or the height of a maize plant in centimetres (1 mark).
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