Instructions
Read each question carefully. For Section 1, choose the best answer. For Section 2, write your answers in the space provided, showing your work where necessary. Good luck!
Section 1: Objective Questions
Answer the following 20 questions.
- What is the value you get when you add up all the numbers in a data set and divide by the count of the numbers?
a) Median
b) Mode
c) Mean
d) Range - What is the middle value in a data set that has been ordered from least to greatest?
a) Mean
b) Median
c) Range
d) Mode - Which term describes the value that appears most often in a data set?
a) Range
b) Mean
c) Mode
d) Median - To find the range of a data set, you:
a) Add all the numbers together.
b) Find the most common number.
c) Find the middle number.
d) Subtract the smallest value from the largest value. - Find the mean of this data set: 2, 8, 5, 3, 7
a) 5
b) 6
c) 25
d) 8 - Find the median of this data set: 10, 4, 8, 12, 6
a) 8
b) 10
c) 6
d) 4 - Find the mode of this data set: 5, 9, 2, 1, 9, 4, 9
a) 5
b) 1
c) 4
d) 9 - Find the range of this data set: 21, 15, 30, 11, 18
a) 15
b) 19
c) 11
d) 30 - What is the median of this data set: 4, 10, 8, 6?
a) 8
b) 6
c) 7
d) 10 - A scatter graph is used to show the relationship between:
a) One set of data.
b) Two sets of data.
c) Data over time.
d) Parts of a whole. - If a scatter graph shows that as one variable increases, the other variable also tends to increase, it has a:
a) Positive correlation
b) Negative correlation
c) No correlation
d) Zero range - On a scatter graph, the relationship between daily ice cream sales and daily temperature would most likely show a:
a) Negative correlation
b) No correlation
c) Positive correlation
d) Mean correlation - If the points on a scatter graph are spread out randomly with no clear pattern, it shows:
a) Positive correlation
b) Negative correlation
c) No correlation
d) A mistake in the data - Which type of chart is best for comparing different categories of data, like the number of students who prefer apples, bananas, or oranges?
a) Line graph
b) Scatter graph
c) Bar chart
d) Tally chart - Which type of graph is best for showing how data changes over a period of time, like the height of a plant over several weeks?
a) Line graph
b) Pie chart
c) Bar chart
d) Scatter graph - A tally chart is most useful for:
a) Calculating the mean.
b) Finding the median.
c) Recording data as it is being collected.
d) Displaying the range. - Find the mean of 10, 20, 30, 40.
a) 20
b) 25
c) 30
d) 100 - What is the range of this data set: 7, 7, 7, 7, 7?
a) 7
b) 35
c) 1
d) 0 - A scatter graph shows that as the number of hours spent watching TV increases, test scores tend to decrease. This is an example of:
a) Positive correlation
b) Negative correlation
c) No correlation
d) A weak relationship - To find the median of a data set with an even number of values, you:
a) Use the larger of the two middle numbers.
b) Use the smaller of the two middle numbers.
c) Find the mean of the two middle numbers.
d) Remove one number to make it odd.
Section 2: Subjective Questions
Answer the following 10 questions. Show your work where needed.
-
A class of 25 students took a spelling test. Their scores out of 10 were:
8, 7, 9, 10, 5, 6, 7, 8, 9, 10, 10, 4, 7, 6, 8, 9, 10, 7, 5, 8, 9, 7, 6, 8, 10
Organize this data in a frequency table.
-
Using the data from question 1, calculate the mean score. (You can round to one decimal place if necessary).
-
Using the data from question 1, find the median score.
-
Using the data from question 1, find the mode score(s).
-
Using the data from question 1, find the range of the scores.
-
You want to find out the favourite type of movie (e.g., comedy, action, sci-fi, animation) among students in your year group. Describe the steps you would take to collect, organize, and represent this data.
-
When would a line graph be a better choice for representing data than a bar chart? Give a specific example.
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Look at this set of data: 5, 6, 7, 8, 99. Calculate the mean and the median. Which one do you think is a better representation of the "typical" number in this set, and why?
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Imagine you are plotting a scatter graph. What kind of correlation (positive, negative, or no correlation) would you expect to see between "the number of hours a person spends practicing a musical instrument each week" and "their level of skill"? Explain your reasoning.
-
The mean score of four friends in a board game is 15. Three of the scores are 12, 18, and 10. What is the fourth friend's score? Show your working.
Answer Key
Section 1: Objective Questions
- c) Mean
- b) Median
- c) Mode
- d) Subtract the smallest value from the largest value.
- a) 5 (Sum = 25, 25 / 5 = 5)
- a) 8 (Ordered: 4, 6, 8, 10, 12)
- d) 9
- b) 19 (30 - 11 = 19)
- c) 7 (Ordered: 4, 6, 8, 10. Middle two are 6 and 8. (6+8)/2 = 7)
- b) Two sets of data.
- a) Positive correlation
- c) Positive correlation
- c) No correlation
- c) Bar chart
- a) Line graph
- c) Recording data as it is being collected.
- b) 25 (Sum = 100, 100 / 4 = 25)
- d) 0 (7 - 7 = 0)
- b) Negative correlation
- c) Find the mean of the two middle numbers.
Section 2: Subjective Questions
-
Frequency Table:
Score Tally Frequency 4 | 1 5 || 2 6 ||| 3 7 ||||| 5 8 ||||| 5 9 |||| 4 10 ||||| 5 Total 25 -
Mean: The sum of all scores is 194. (4x1 + 5x2 + 6x3 + 7x5 + 8x5 + 9x4 + 10x5 = 4+10+18+35+40+36+50 = 194).
194 / 25 = 7.76. -
Median: With 25 students, the median is the 13th score when ordered.
Ordered scores: 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10.
The median score is 8. - Mode: The scores that appear most often are 7, 8, and 10 (each appears 5 times). This data set is trimodal.
- Range: Highest score (10) - Lowest score (4) = 6.
-
Example Answer:
Collect: I would create a survey asking "What is your favourite movie genre?" with options like Comedy, Action, Sci-Fi, and Animation. I would give this survey to all students in my year.
Organize: I would use a tally chart to count the votes for each genre.
Represent: I would use a bar chart to display the results, as it is good for comparing the popularity of different categories. Each bar would represent a genre, and its height would show how many students chose it. -
Example Answer: A line graph is better than a bar chart when you want to show a trend or change over a continuous period of time.
Example: Tracking the temperature outside every hour for a full day. A line graph would clearly show how the temperature rises and falls over the 24-hour period. A bar chart would not show this continuous change as effectively. -
Calculation:
Mean: (5 + 6 + 7 + 8 + 99) / 5 = 125 / 5 = 25.
Median: The numbers are already in order. The middle number is 7.
Explanation: The median (7) is a better representation of the typical number. The number 99 is an outlier (a value much higher than the others) and it pulls the mean up, making it much higher than most of the numbers in the set. The median is not affected by outliers. -
Example Answer: I would expect to see a positive correlation.
Reasoning: As the amount of time someone spends practicing (one variable) increases, their skill level (the second variable) is also likely to increase. More practice generally leads to better performance. -
Working:
The mean of four scores is 15.
Total score = Mean × Number of friends = 15 × 4 = 60.
The sum of the three known scores = 12 + 18 + 10 = 40.
The fourth score = Total score - Sum of known scores = 60 - 40 = 20.
The fourth friend's score is 20.