Statistical Methods

16 Grade 10 Geography questions on Statistical Methods, with worked marking schemes. 16 questions are available on this topic in full.

1. Question 1

   3 marks

   The numbers of 90 kg bags of maize harvested on a farm in Trans Nzoia in five successive seasons were 120, 145, 130, 160 and 145.

   (a) Calculate the mean harvest per season.

   (b) State the mode of the data.

   (3 marks)

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2. Question 2

   1 mark

   The numbers of 90 kg bags of maize sold by a trader in six market seasons were recorded in this order: 40, 52, 45, 60, 48, 57. What is the median number of bags?

   A. 48

   B. 57

   C. 50

   D. 52.5

   (1 mark)

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3. Question 3

   1 mark

   A class studying the types of shops in a town centre recorded details of every fifth shop along the main street, starting with the third shop. Which sampling method were they using?

   A. Purposive sampling

   B. Stratified sampling

   C. Systematic sampling

   D. Random sampling

   (1 mark)

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4. Question 4

   3 marks

   Suggest three reasons why a geographer collecting data on the types of shops in a large town would sample rather than study every shop.

   (3 marks)

   Marking scheme

   Any THREE of the following, 1 mark each: the total number of shops is too large to be covered by one person or one class; sampling saves time, since the study can be completed within the period available; sampling saves money spent on travel, printing and labour; a smaller amount of data is easier to record, sort and analyse without errors; a well chosen sample still gives results that represent the whole town fairly accurately. Maximum 3 marks.

5. Question 5

   1 mark

   A learner wishes to present data showing how the total area of a farm in Kirinyaga is shared among coffee, bananas, napier grass and the homestead, so that each share is seen as part of the whole. Which method of presentation is the most suitable?

   A. A divided circle

   B. A simple line graph

   C. A wind rose

   D. A dot map

   (1 mark)

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6. Question 6

   1 mark

   A class is investigating the quantity of fish landed at beaches along Lake Victoria. Which one of the following would provide them with secondary data?

   A. Copying landing figures from the county fisheries office records

   B. Interviewing the fishermen as they land their catch

   C. Counting the crates of fish unloaded at the beach

   D. Observing the number of boats returning each morning

   (1 mark)

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7. Question 7

   3 marks

   State three reasons why geographers present raw statistical data in graphs instead of leaving it in tables of figures.

   (3 marks)

   Marking scheme

   Any THREE of the following, 1 mark each: graphs show trends, rises and falls at a glance; comparison between items or between years is quicker; graphs are easier and more attractive to read for a person who is not used to figures; large amounts of data are summarised into one small space; relationships between two sets of values can be seen more easily; values not actually recorded can be read off between plotted points. Maximum 3 marks.

8. Question 8

   4 marks

   Explain four ways in which statistical data is useful to a county government when planning for agriculture.

   (4 marks)

   Marking scheme

   Any FOUR of the following, 1 mark each, where the use is explained and not merely named: production figures show trends over the seasons, so the county can tell whether output is rising or falling; data reveals wards where harvests are low, so relief food or subsidised inputs can be directed there; past figures allow the county to forecast future output and set realistic production targets; comparison between wards or crops shows where investment such as irrigation or storage will pay best; figures on acreage and yields form the basis for preparing the agricultural budget and ordering inputs such as fertiliser; data collected before and after a project is used to monitor and evaluate whether the project succeeded. Maximum 4 marks.

9. Question 9

   1 mark

   On seven market days, a farmer in Narok sold the following numbers of goats: 12, 15, 12, 18, 20, 12 and 15. What is the mode of this set of data?

   A. 12

   B. 8

   C. 20

   D. 15

   (1 mark)

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10. Question 10

    1 mark

    The maximum daily temperatures recorded at a school weather station for five days were 29 °C, 33 °C, 27 °C, 31 °C and 30 °C. What is the range of these temperatures?

    A. 30 °C

    B. 33 °C

    C. 27 °C

    D. 6 °C

    (1 mark)

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11. Question 11

    1 mark

    Five tea pickers on an estate in Kericho picked the following amounts of green leaf in one day: 24 kg, 31 kg, 28 kg, 35 kg and 27 kg. What is the mean amount picked per worker?

    A. 28 kg

    B. 31 kg

    C. 11 kg

    D. 29 kg

    (1 mark)

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12. Question 12

    2 marks

    Distinguish between the mean and the median as measures of central tendency.

    (2 marks)

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13. Question 13

    3 marks

    Explain three limitations of using the mode to describe a set of geographical data.

    (3 marks)

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14. Question 14

    1 mark

    In a village, nine farmers each harvested between 8 and 12 bags of beans, while a tenth farmer, who owns a large irrigated plot, harvested 90 bags. Why would the mean be a poor measure of the typical harvest in this village?

    A. The single very large value raises the mean far above what most farmers harvested

    B. The mean can only be used when all the values are equal

    C. The mean cannot be worked out when the number of values is even

    D. The mean is always smaller than the smallest value in a set of data

    (1 mark)

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15. Question 15

    6 marks

    Outline the steps a Grade 10 class would follow in collecting and presenting data on the means of transport used by learners to get to school.

    (6 marks)

    Marking scheme

    Any SIX steps, 1 mark each, and they must be in a sensible order: state the objective of the study, that is, to find out the means of transport used; decide on the categories to be recorded, for example walking, boda boda, matatu, bicycle and private car; prepare a recording instrument such as a tally sheet or a short questionnaire; agree on where and for how long the recording will be done, for example at the gate for one week; collect the data by tallying each learner or by asking each learner in turn; add up the tallies to obtain the total for each means of transport; choose a suitable method of presentation, for example a bar graph or a divided circle; select a suitable scale, draw the graph and label it fully with a title and a key; interpret the finished graph and write the conclusion. Maximum 6 marks.

16. Question 16

    2 marks

    In a survey of 60 learners, 20 said they travel to school by matatu. Calculate the angle that would represent matatu users on a divided circle.

    (2 marks)

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