Statistics 1

14 Grade 10 Essential Mathematics questions on Statistics 1, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   3 marks

   A teacher organises the marks scored by learners in a test into the classes 10–19, 20–29, 30–39 and so on. State the class width and the mid-point of the class 30–39, and explain one advantage of grouping the marks in this way.

   (3 marks)

   Marking scheme

   1 mark: class width = 10 (accept working using boundaries 29.5 to 39.5). 1 mark: mid-point of 30–39 = (30 + 39)/2 = 34.5. 1 mark for any one advantage: a large number of marks is reduced to a few classes that are easier to handle; the pattern of performance, such as where most learners scored, is seen more easily; it makes drawing and reading a graph of the results simpler.

2. Question 2

   4 marks

   In a mathematics test, the mean mark of the 20 boys in a class was 62 and the mean mark of the 12 girls was 70. Calculate the mean mark of the whole class.

   (4 marks)

   Marking scheme

   Total marks for the boys = $20\times 62=1$,240 (1 mark); total marks for the girls = $12\times 70=840$ (1 mark); total marks = 1,240 + 840 = 2,080 and total number of learners = 20 + 12 = 32 (1 mark); mean mark for the class = 2,$080÷32=65$ marks (1 mark). Award zero for the last two marks if the candidate simply averages 62 and 70 to get 66.

3. Question 3

   3 marks

   The masses, in kilogrammes, of nine bunches of bananas harvested on a farm in Kisii were 20, 12, 26, 15, 12, 30, 18, 12 and 22. Determine the median mass and the modal mass.

   (3 marks)

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4. Question 4

   3 marks

   A household shares its monthly income among food, rent, school fees and savings. Explain why a pie chart is a suitable way of displaying this information, and state one limitation of using a pie chart.

   (3 marks)

   Marking scheme

   1 mark: the whole circle represents the total monthly income, so each sector shows what share of the income goes to one item. 1 mark: the shares can be compared at a glance as proportions of the whole, since the four sectors add up to the complete circle (360°). 1 mark for any one limitation: sectors of nearly equal size are difficult to compare by eye; the actual amounts in shillings are not shown unless they are written on the chart; it becomes crowded and unclear if there are many items; it cannot show how the spending changes from month to month.

5. Question 5

   1 mark

   The daily maximum temperatures, in degrees Celsius, recorded at a weather station in Nyeri during one week were 24, 21, 27, 19, 25, 23 and 26. What is the range of the temperatures?

   A. 8

   B. 19

   C. 23.6

   D. 46

   (1 mark)

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6. Question 6

   1 mark

   A Grade 10 class wishes to find out the means of transport most commonly used by learners in the class to travel to school. Which method of collecting the data is most appropriate?

   A. Measuring the distance from each learner's home to the school

   B. Counting the vehicles that pass the school gate in one hour

   C. Reading a textbook chapter about means of transport in Kenya

   D. Administering a short questionnaire to every learner in the class

   (1 mark)

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7. Question 7

   3 marks

   In a Grade 10 class the number of brothers and sisters of each learner was recorded. Six learners had 1 sibling, ten had 2 siblings, nine had 3 siblings and five had 4 siblings. Calculate the mean number of siblings per learner, correct to 1 decimal place.

   (3 marks)

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8. Question 8

   3 marks

   The mean of a shop's daily sales over five days was KSh 4,600. The sales on four of the days were KSh 4,200, KSh 5,100, KSh 3,900 and KSh 4,800. Calculate the sales on the fifth day.

   (3 marks)

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9. Question 9

   1 mark

   In a small market, one trader earns KSh 90,000 on a busy day, while each of the other nine traders earns a different amount between KSh 800 and KSh 1,500 on the same day. Which average best describes the typical daily earnings of a trader in that market?

   A. The median, because it is not pulled up by the one very large amount

   B. The mean, because it makes use of every trader's earnings

   C. The mode, because it is the amount that occurs most often in the list

   D. The range, because it shows how far apart the earnings are

   (1 mark)

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10. Question 10

    1 mark

    Of the 720 learners in a school, 240 live within 2 km of the school. If this information is represented on a pie chart, what is the angle of the sector representing the learners who live within 2 km?

    A. 60°

    B. 33.3°

    C. 120°

    D. 240°

    (1 mark)

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11. Question 11

    1 mark

    In a survey of 30 households in a village in Vihiga, the number of chickens kept by each household was recorded. Four households kept 2 chickens, nine kept 3 chickens, eleven kept 4 chickens and six kept 5 chickens. What is the modal number of chickens kept?

    A. 2

    B. 3.6

    C. 11

    D. 4

    (1 mark)

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12. Question 12

    1 mark

    The numbers of goats sold by a livestock trader in Garissa on seven market days were 12, 9, 15, 9, 20, 11 and 14. What is the median number of goats sold?

    A. 9

    B. 12.9

    C. 12

    D. 11

    (1 mark)

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13. Question 13

    2 marks

    Distinguish between primary data and secondary data, giving one example of each.

    (2 marks)

    Marking scheme

    1 mark: primary data is data collected first-hand by the researcher for the particular study, e.g. marks the learner records by interviewing classmates or by measuring the height of each learner. 1 mark: secondary data is data obtained from a source where it has already been collected and recorded by someone else, e.g. population figures taken from a KNBS report, a newspaper or a school register. A candidate who only defines one of the two earns 1 mark.

14. Question 14

    1 mark

    A shopkeeper in Nyahururu recorded the number of exercise books sold on each of six days as 15, 12, 40, 18, 15 and 20. Calculate the mean number of exercise books sold per day.

    A. 17.1

    B. 15

    C. 20

    D. 16.5

    (1 mark)

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