Multiple Choice

1. Which of the following data sets represents a discrete numerical variable?

   The height of students in a class.

   The number of siblings each student has.

   The temperature outside measured hourly.

   The amount of milk in a carton.

2. Which of the following is an example of a continuous numerical variable?

   The weight of apples harvested from an orchard.

   The score a student gets on a $10$-question quiz.

   The number of days it rained in a month.

   The number of cars in a parking lot.

3. A group of students recorded the number of hours they spent reading last week: $3, 5, 2, 4, 5, 3, 5, 6, 1$. What is the mode of this data set?

   $4$

   $5$

   $6$

   $3$

4. The daily high temperatures for a week in degrees Celsius were: $18, 22, 20, 19, 25, 23, 20$. What is the range of these temperatures?

   $5$

   $7$

   $20$

   $19$

5. The number of points scored by a basketball team in their last $6$ games were: $78, 85, 92, 75, 80, 88$. What is the median number of points scored?

   $83.5$

   $82.5$

   $80$

   $85$

6. The ages of $7$ employees at a small company are: $25, 32, 45, 28, 50, 30, 35$. What is the median age of the employees?

   $35$

   $30$

   $32$

   $32.5$

7. A student's scores on $5$ math quizzes are: $85, 90, 78, 92, 80$. What is the mean score for these quizzes?

   $87$

   $80$

   $85$

   $90$

8. A shoe store wants to determine the most popular shoe size to order for their next shipment. Which measure of central tendency would be most useful?

   Mean

   Median

   Mode

   Range

9. A real estate agent is reporting the typical price of homes sold in a neighbourhood where a few very expensive homes were recently sold, potentially skewing the average. Which measure of central tendency would be most appropriate to give a fair representation of typical home prices?

   Median

   Mean

   Range

   Mode

10. A teacher wants to calculate the average performance of her class on a math test, where the scores are generally evenly distributed without significant outliers. Which measure of central tendency would be the most suitable?

    Mode

    Range

    Mean

    Median

11. A group of Grade 7 students had the following scores on a math quiz: $75, 80, 85, 90, 70$. What is the mean score for these students?

    $80$

    $78$

    $85$

    $82$

12. A scientist measured the heights in cm of seven bean sprouts: $12, 15, 11, 13, 16, 14, 10$. What is the median height of these bean sprouts?

    $14$

    $13$

    $12$

    $15$

13. A survey asked nine Grade 7 students how many siblings they have. The responses were: $1, 2, 0, 3, 1, 2, 1, 0, 4$. What is the mode of this dataset, representing the most common number of siblings?

    $2$

    $0$

    $4$

    $1$

14. The daily maximum temperatures in a city for five days were recorded as: $18^\circ C, 22^\circ C, 15^\circ C, 25^\circ C, 20^\circ C$. What is the range of these temperatures?

    $8$

    $7$

    $9$

    $10$

15. Six friends played a video game and their scores were: $50, 60, 55, 70, 65, 50$. What is the median score for this group of friends?

    $60$

    $57.5$

    $55$

    $58$

16. A local bakery records the number of loaves of bread sold each day for a week: $120, 135, 110, 125, 140, 115, 250$. The manager wants to describe the typical daily sales but is concerned about a specific day's sales affecting the representation. Which measure of central tendency would be LEAST affected by the outlier in this dataset and why?

    Range, because it shows the spread of data.

    Mode, because it represents the most frequent value.

    Median, because it represents the middle value when data is ordered, making it less sensitive to extreme values.

    Mean, because it averages all values equally.

17. A teacher recorded the time (in minutes) it took for students to complete a math quiz: $8, 12, 10, 15, 9, 11, 13, 10, 16, 14$. If two new students finished the quiz very quickly, in $5$ minutes and $6$ minutes respectively, how would the mean and median of the completion times likely change?

    The mean would decrease, but the median would remain the same.

    Both the mean and median would decrease significantly.

    The mean would decrease, and the median would decrease slightly.

    Both the mean and median would increase.

18. The number of goals scored by a soccer team in their last $10$ games are: $2, 1, 3, 0, 2, 4, 1, 2, 0, 3$. What is the difference between the mean and the mode of this dataset?

    $0.4$

    $0.1$

    $0.3$

    $0.2$

19. A small company has $5$ employees with salaries (in dollars) of: $30000, 32000, 35000, 38000, 150000$. The owner wants to present a "typical" salary that makes the company seem fair to potential new hires, without highlighting the extremely high salary of the owner. Which measure of central tendency would be the most suitable to use for this purpose?

    Mean, because it considers all salaries.

    Median, because it minimizes the effect of the owner's outlier salary.

    Mode, because it shows the most common salary.

    Range, because it shows salary variation.

20. A student measures the temperature ($^\circ C$) outside their house every day for a week: $18, 20, 22, 19, 21, 18, 20$. If they mistakenly recorded one day's temperature as $2^\circ C$ instead of $20^\circ C$, how would this error affect the range and the mode compared to the original (correct) dataset?

    The range would decrease, and the mode would remain the same.

    The range would remain the same, and the mode would change.

    The range would decrease, and the mode would change.

    The range would increase, and the mode would change.

21. Consider two datasets:

    Dataset B has a higher mean and a higher median than Dataset A.

    Dataset B has the same mean but a higher median than Dataset A.

    Dataset A has a higher mean and a higher median than Dataset B.

    Dataset A has a higher mean but the same median as Dataset B.

22. A new amusement park wants to claim it has a "typical" ride wait time of $15$ minutes. They collect data on wait times (in minutes) for $8$ rides: $5, 10, 12, 15, 18, 20, 25, x$. If they want the mean wait time to be exactly $15$ minutes, what must be the value of $x$?

    $5$

    $12$

    $10$

    $15$

23. A local library recorded the number of books borrowed by visitors in one hour: $1, 3, 2, 4, 1, 5, 2, 3, 1, 6$. After calculating the mean, median, and mode, which of these measures represents a discrete variable, and which statement about its calculation is true for this dataset?

    The median is a discrete value and represents the most frequent borrowing number.

    The mean is a discrete value and always exactly one of the data points.

    The mean is a continuous value that can be a decimal, while the number of books borrowed is discrete.

    The mode is a discrete value but might not be useful if all values are unique.

24. A fruit stand sells apples in bags, and the number of apples in $10$ randomly selected bags are: $5, 6, 5, 7, 8, 6, 5, 9, 6, 5$. Which measure of central tendency would be least appropriate to describe the 'typical' number of apples in a bag, given that the distribution is slightly skewed?

    Mean, because it is pulled towards the longer tail of the distribution, misrepresenting the center.

    Range, because it only shows spread, not central tendency.

    Mode, because it identifies the most frequent number.

    Median, because it is resistant to skewness.

25. The heights (in cm) of $7$ plants are: $15, 18, 20, 16, 22, 19, 17$. If two more plants are added with heights $25$ cm and $13$ cm, which measure of central tendency will change the most relative to its original value, and why?

    The median, because the middle position changes with the addition of new data points.

    The mode, because new values can easily create a new mode or remove an old one.

    The mean, because every new value directly impacts its calculation.

    The range, because adding extreme values can significantly increase its value.

26. A sports team scored the following points in $5$ games: $12, 18, 15, x, 22$. The mean score for these $5$ games was $17$. What is the range of the scores?

    $9$

    $12$

    $10$

    $8$

27. Eight students recorded the number of books they read last month: $3, 5, 2, 7, 3, 6, 4, 3$. What is the median number of books read? If the student who read $7$ books actually read $1$ book, what would be the new median?

    Original median: $4$; New median: $3$

    Original median: $3.5$; New median: $3$

    Original median: $3$; New median: $3.5$

    Original median: $3$; New median: $2.5$

28. A small business recorded the number of items sold each day over a week: $25, 28, 22, 150, 25, 24, 23$. Which statement best summarizes the measures of central tendency and the most useful 'typical' measure for this week?

    Mean $=25$; Median $=25$; Mode $=25$; Most useful: Mode ($25$).

    Mean $\approx 42.43$; Median $=25$; Mode $=25$; Most useful: Median ($25$).

    Mean $\approx 42.43$; Median $=24$; Mode $=25$; Most useful: Median ($24$).

    Mean $\approx 42.43$; Median $=25$; Mode $=25$; Most useful: Mean ($\approx 42.43$).

29. Class A has $20$ students with an average (mean) test score of $78\%$. Class B has $25$ students with an average (mean) test score of $85\%$. When the scores of both classes are combined, what is the overall average (mean) test score for all students, rounded to one decimal place?

    $81.6\%$

    $81.9\%$

    $82.1\%$

    $82.5\%$

30. The average weight of $4$ packages is $2.8$ kg. When a fifth package is added, the average weight of all $5$ packages becomes $3.1$ kg. If the first four packages weighed $2.5$ kg, $3.0$ kg, $2.7$ kg, and $3.0$ kg, what is the range of the five package weights?

    $2.0$ kg

    $1.8$ kg

    $1.5$ kg

    $1.7$ kg

Numerical

31. A baker recorded the number of cakes sold each day for a week: $18, 22, 15, 20, 25, x, 17$. If the mean number of cakes sold per day for the entire week was $20$, what is the median number of cakes sold per day for the week?

32. A group of $10$ students had an average (mean) score of $78\%$ on a math test. Another group of $5$ students had an average score of $84\%$ on the same test. When these two groups are combined, what is the overall average score for all $15$ students? Round your answer to the nearest whole number percentage.

33. The heights (in cm) of a group of seven basketball players are recorded as follows: Two players are $190$ cm tall, three players are $195$ cm tall, one player is $200$ cm tall, and one player is $185$ cm tall. What is the sum of the median height and the modal height of these players?

34. A dataset consists of five numbers: $12, 18, 15, 23, x$. If the range of this dataset is $15$ and $x$ is the smallest number in the set, what is the value of $x$?

35. A small company has $5$ employees. Their monthly salaries are: $\$2500, \$2800, \$3000, \$3200, \$15000$. Which measure of central tendency (mean, median, or mode) best represents a typical employee's salary in this company, and what is its value?