Grade 10 essential mathematics – Statistics I Quiz
1. Which of the following is an example of primary data in a school survey?
Primary data are collected first-hand for the specific study. Asking Form 3 students directly produces original data, while the other items are existing secondary sources.
2. Which variable is qualitative (categorical)?
Qualitative variables describe categories or qualities (e.g. colour). The others are quantitative (numerical) measurements.
3. Which quantity is a discrete variable?
Discrete variables take countable values (whole numbers). Number of students is counted as whole persons, while height, temperature and time are continuous measurements.
4. Which measure of central tendency is best for a heavily skewed distribution?
The median (middle value) is less affected by extreme values (outliers) and skewness, so it better represents the centre of a skewed distribution than the mean.
5. In a test, 4 students scored 10, 6 scored 15 and 10 scored 20. What is the mean score?
Mean = (4×10 + 6×15 + 10×20) ÷ 20 = (40 + 90 + 200) ÷ 20 = 330 ÷ 20 = 16.5.
6. What is the median of the marks 12, 15, 20, 22?
With four values (even number), the median is the average of the two middle numbers: (15 + 20) ÷ 2 = 17.5.
7. What is the mode of the data 2, 2, 3, 4, 2, 5?
The mode is the value that appears most often. Here 2 appears three times, more than any other value.
8. What is the range of the numbers 5, 8, 12, 20?
Range = maximum − minimum = 20 − 5 = 15.
9. A set of scores ranges from 12 to 55. If you want about 8 equal classes for a frequency table, what is a suitable class width?
Range = 55 − 12 = 43. Class width ≈ 43 ÷ 8 = 5.375. We round up to a convenient whole number, 6, to cover all data.
10. If the cumulative frequency for scores ≤ 50 is 120, what does this mean?
Cumulative frequency at a value gives the total number of observations with scores less than or equal to that value.
11. Which chart is best to show how a total number of students is split into different subjects as percentages?
Pie charts display parts of a whole as percentages or fractions, making them suitable for showing subject shares of the total.
12. Which graph is appropriate for continuous data grouped into class intervals (e.g., heights)?
Histograms display continuous data in adjacent bars representing class intervals. Bar charts are for separate categories, not continuous intervals.
13. What is one main advantage of a stem-and-leaf diagram over a histogram?
Stem-and-leaf plots show individual data points while grouping, so you can still see the original values. Histograms do not retain exact values.
14. If a dataset has one very large outlier, which measure is least affected?
The median is based on position, so a single extreme value has little effect on it. The mean, range and sum are strongly affected by outliers.
15. Which description matches stratified sampling?
Stratified sampling ensures representation from each subgroup by dividing the population into strata and sampling randomly within each.
16. Which sampling method is most likely to produce a biased sample?
Sampling only maths club members will likely bias results because their views may not represent all students. The other methods are examples of random or systematic sampling that reduce bias.
17. A bag contains 3 red balls and 2 blue balls. What is the probability of drawing a red ball at random?
Probability of red = number of red balls ÷ total balls = 3 ÷ (3+2) = 3/5.
18. If a fair die is rolled 40 times, approximately how many times would you expect a six to occur?
Expected number = probability of six (1/6) × number of trials 40 = 40 ÷ 6 ≈ 6.666..., written approximately as 6.7.
19. If a boxplot shows the median closer to the lower quartile (Q1) than to the upper quartile (Q3), what does this suggest about the distribution?
If the median is nearer Q1, the upper half is more spread out, indicating a long tail to the right (positive skew).
20. What is the relationship between variance and standard deviation?
By definition, variance is the average squared deviation from the mean; standard deviation is the square root of that variance, giving a measure in the original units.
21. In a class of 30 pupils, 12 are girls. What is the relative frequency of girls in the class?
Relative frequency = number of girls ÷ total = 12 ÷ 30 = 0.4 (which is 40%).
22. What is the formula for the arithmetic mean of n observations x1, x2, ..., xn?
The arithmetic mean is the sum of all observations divided by the number of observations.
23. Which measure of central tendency is most appropriate to summarise the favourite subject (e.g., Maths, Science, English) of students?
For categorical data (favourite subject), the mode (the most common category) summarises the data; mean and median do not apply to categories.
24. Which scatter plot pattern indicates a positive correlation between two variables (e.g., height and shoe size)?
A positive correlation shows that as one variable increases, the other also increases, producing an upward trend on the scatter plot.
25. If the probability of rain tomorrow is 0.3, what is the probability that it will not rain?
The complement rule: probability it will not rain = 1 − probability it will rain = 1 − 0.3 = 0.7.