Question 1:
Answer the following multiple-choice questions. Simply indicate the correct answer next to the question number. E.g., 1.11 e)
- The mode of a data set represents:
- The mid-point number of a data set, if arranged from smallest to largest.
- The average value of a data set.
- The most common number that appears in a data set.
- None of the above
- The mean of a data set represents:
- The most common number that appears in a data set.
- The mid-point number of a data set, if arranged from smallest to largest.
- The average value of a data set.
- None of the above
- The median of a data set represents:
- The most common number that appears in a data set.
- The mid-point number of a data set, if arranged from smallest to largest.
- The average value of a data set.
- None of the above
- For the data set 8, 3, 5, x, 2, 4, 9, 11. What must the value of x be, such that the mean of the data set is 7?
- 7
- 14
- 21
- 28
- Which of the following is true regarding the dataset 11, 4, 2, 9, 5, 6, 2, 1:
- The mean is 5
- The data is multi-modal
- The mode is 4.5
- All of the above
- Which of the following is true regarding the normal distribution of data?
- Normal distribution, also known as the Bernoulli distribution, is a probability distribution that is symmetric about the standard deviation, showing that data near the mean are more frequent in occurrence than data far from the mode.
- Normal distribution, also known as the Poisson distribution, is a probability distribution that is symmetric about the standard deviation, showing that data
near the standard deviation are more frequent in occurrence than data far from the standard deviation.
- Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
- Normal distribution, also known as the T-Distribution distribution, is a probability distribution that is symmetric about the mode, showing that data near the mode are more frequent in occurrence than data far from the mode.
- A standard deck of cards contains 52 cards, whereas a deck of cards with Jokers contains 54 cards. The probability of selecting a red Jack from a deck of cards which excludes Jokers is compared to a deck with Jokers.
- increased
- decreased
- unchanged
- none of the above
- For the data set 1, 2, 3, 3, 5, 7, 9, 10, the Mode + Median + Mean equals:
- 11
- 9
- 13
- 12
- There are 67 members of a virtual book club. Three new males and four females are admitted to the book club. By what percentage have the total number of members increased, correct to two decimal places?
- 8,00%
- 8,70%
- 10,45%
- 2,70%
- Which measure of central location is not affected by outliers?
- Mean
- Mode
- Median
- Standard deviation
Question 2:
- Define the following terms:
- Categorical variable (2)
- Continuous variable: (2)
- Normal distribution: (2)
- Quantitative data (2)
- Qualitative data (2)
- Copy the table below. For each of the following questions, state:
- The type of random variable, i.e., qualitative or quantitative.
- The scale of measurement, i.e., nominal, ordinal, interval or ratio.
- Whether the random variable is discrete or continuous.
| Q. | a) Type of Value | b) Scale of Measurement | c) Discrete/Continuous |
| E.g., 2.2.6 | Quantitative | Ordinal | Discrete |
| 2.2.1 | |||
| 2.2.2 | |||
| 2.2.3 | |||
| 2.2.4 | |||
| 2.2.5 |
- The brands of chocolates in a supermarket e.g., Cadbury, Lindt, Beacon. (3)
- The mark obtained in an assignment, e.g., 37.5%, 56.25%, 81.25%. (3)
- The number of units of blood transported from the SANBS to Helen Joseph Hospital on a Monday morning, e.g., 51, 211, 315. (3)
- The classification of types of eggs, e.g., small, medium, jumbo. (3)
- The rating of service received from the Department of Home Affairs on a
scale from 1 to 10, with 1 representing “Very Poor” and 10 representing
“Excellent”, e.g., 3, 5, 8. (3)
- A company has manufactured a total of 233,215 specialised nuts for Ford South Africa to date, with an average diameter of 11mm. To test if the diameter is truly 11 mm, 500 nuts were randomly selected for inspection. The average diameter for the sample was found to be 11.5mm.
- State the random variable of interest (X). (1)
- Give the symbol for the population size and state what it is equal to. (1)
- Give the symbol for the population average and state what it is equal to. (1)
- Give the symbol for the sample size and state what it is equal to. (1)
- Give the symbol for the sample average and state what it is equal to. (1)
Question 3:
- The Hope Foundation has eight volunteers crocheting dolls during the week to be sold at the weekly weekend market in Melville.
| Volunteer: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Number of dolls crochet during the week. | 19 | 16 | 22 | 23 | 15 | 22 | 15 | 26 |
| Have all dolls been sold by the weekend? | Yes | No | Yes | Yes | Yes | Yes | Yes | No |
Calculate the probability that a randomly selected volunteer will:
- crochet 22 dolls. (2)
- crochet 23 dolls (2)
- have all their dolls sold by the weekend. (2)
- crochet more than 18 dolls and will not have all of them sold by the weekend. (3)
- crochet more than 19 dolls and will have all of them sold by the weekend.
(3)
- At the Houghton Country Club, the ages of the golf players for the first four 4- balls on a particular Saturday are noted:
13 11 39 19 43 29 38 61 39 42 51 23 21 82 31 45
- Calculate the mean age of the 16 golfers (2). Interpret your answer (1). (3)
- Calculate the median age of the 16 golfers (2). Interpret your answer (1). (3)
- State the modal age of the 16 golfers. (2) Interpret your answer (1). (3)
- Calculate the standard deviation for the ages of the golfers. (4)
- Calculate Pearson’s median skewness coefficient for the ages of the 16 golfers.
(2) Interpret your answer (1). (3)
- Which measure of central location would you use in your reporting – the mean, median or mode? Motivate your answer. (2)
Question 4:
- Engen convenience stores have conducted an analysis on chocolates sold per patron between 24:00-06:00, weekdays. The analysis revealed that the spending distribution can be approximated as Normal with a mean of R37,19 and a standard deviation of R9.26. What percentage of customers will spend less than R35.00 on chocolates? (5)
- Suppose the circumference of a bolt used in the new Ford Ranger bakkie built in Tshwane follows a normal distribution with X ∼ N(15, 6). If one of these bolts was randomly selected for quality control, find the probability that its circumference will be larger than 17.4mm. (5)
- Suppose that the South African National Defence Force employs 10,000 Officers, each earning a unique remuneration based on their tenure and qualifications. The remuneration is generally distributed with the population mean of µ = R65,000 per month, and the population standard deviation σ = R10,000. What will be the probability of a randomly selected Officer earning more than R55,000 per month? (5)
Question 5:
At Huletts sugar, their production line fills a bag on average with 5kg of sugar and a standard deviation of 0.17kg. The production line manager sampled 100 bags of sugar at random from the production line and found that the average mass of sugar for the 100 bags was 5.012 kg.
- State the mean of the sampling distribution of the sample mean. (2)
- Calculate the standard error of the sampling distribution of the sample mean. (3)
- Calculate the corresponding z-score for the sample mean of 5.012 kg. (3)
Question 6:
The following is a breakdown of Makro Woodmead’s monthly sales of large
appliances.
| Large Appliance | Monthly Sale |
| Dishwasher | 278 |
| Tumble Dryer | 314 |
| Washing Machine | 395 |
| Fridge | 247 |
| Stove | 298 |
- Summarise the large appliance sales with a pivot chart in Microsoft Excel. Display the results using a simple bar graph. Include a copy of your pivot table with your answer. The graph should contain a suitable heading, and all axes should be clearly labelled.
Answers to Above Questions on Statistics
Answer 1: The mode of a dataset represent: The most common number that appears in a data set.
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