Multiple Choice

1. Why is measuring data variability (spread) important when analyzing a set of numbers?

   It only confirms the mode (most frequent number).

   It helps determine the sum of all the numbers.

   It shows how spread out or clustered the data points are.

   It identifies the exact middle point of the data.

2. What is the simplest measure of variability, calculated by finding the difference between the largest and smallest values in a dataset?

   The Median ($Q_2$)

   The Mean

   The Range

   The Interquartile Range (IQR)

3. Calculate the Range for the following dataset: $12, 5, 20, 8, 15$.

   $15$

   $12$

   $10$

   $8$

4. A student scored the following points on five quizzes: $40, 50, 10, 35, 25$. What is the Range of their scores?

   $25$

   $30$

   $40$

5. If a dataset has a maximum value of $150$ and a minimum value of $10$, what is the Range?

   $10$

   $160$

   $140$

6. Two classes scored the same average (mean) on a test. Class A had a Range of $10$, and Class B had a Range of $35$. What does the Range tell us?

   Class B's scores were more spread out than Class A's scores.

   Class A had better scores overall.

   Both classes had the same level of variation.

   Class B had a higher median score.

7. The number of siblings reported by students are: $0, 3, 1, 2, 4, 1$. Calculate the Range of the number of siblings.

   $2$

   $4$

   $3$

8. Which step MUST be completed first before calculating the median or quartiles?

   Order the data from least to greatest.

   Determine the mode.

   Find the largest and smallest values.

   Calculate the sum of all values.

9. The Median ($Q_2$) is essential for calculating the IQR. What percentage of the data falls below the Median?

   $25\%$

   $75\%$

   $50\%$

   $100\%$

10. Find the Median ($Q_2$) of the following ordered dataset: $1, 5, 8, 10, 15$.

    $10$

    $5$

    $8$

    $15$

11. Find the Median ($Q_2$) of the following dataset: $12, 18, 5, 25, 10, 30$.

    $18$

    $16$

    $12$

    $15$

12. What is another name for the Median in the context of calculating data variability?

    The average

    The Range

    The second quartile ($Q_2$)

    The first quartile ($Q_1$)

13. Calculate the Median ($Q_2$) for the dataset: $7, 10, 1, 5, 12, 3$.

    $6.5$

    $7$

    $6$

    $5$

14. If a dataset has $9$ data points, which ordered position represents the Median ($Q_2$)?

    The $5.5^{th}$ position

    The $6^{th}$ position

    The $4^{th}$ position

    The $5^{th}$ position

15. The Lower Quartile ($Q_1$) is the median of which part of the data?

    The entire dataset

    The values larger than $Q_2$

    The top $50\%$ of the data

    The lower half of the data

16. For the dataset $2, 4, 6, 8, 10, 12, 14$, the Median ($Q_2$) is $8$. What is the lower half of the data used to calculate $Q_1$?

    $2, 4, 6, 8, 10$

    $2, 4, 6$

    $2, 4, 6, 8$

17. Calculate the Lower Quartile ($Q_1$) for the ordered dataset: $10, 20, 30, 40, 50$.

    $15$

    $30$

    $20$

    $25$

18. Calculate the Upper Quartile ($Q_3$) for the ordered dataset: $1, 2, 3, 4, 5, 6, 7$.

    $6$

    $4$

    $6.5$

    $5$

19. A dataset has $8$ points: $10, 20, 30, 40, 50, 60, 70, 80$. The Median ($Q_2$) is $45$. What is the value of the Upper Quartile ($Q_3$)?

    $65$

    $55$

    $60$

20. The Upper Quartile ($Q_3$) marks the point where what percentage of the data is equal to or less than that value?

    $75\%$

    $25\%$

    $100\%$

    $50\%$

21. If the data points in the lower half are $10, 15, 20, 25$, how is the Lower Quartile ($Q_1$) calculated?

    The average of $15$ and $20$

    It is $15$

    The average of $10$ and $25$

22. What does the Interquartile Range (IQR) specifically measure?

    The spread of the entire dataset.

    The spread of the middle $50\%$ of the data.

    The spread of the bottom $25\%$ of the data.

    The difference between the mean and the median.

23. Which formula correctly defines the Interquartile Range (IQR)?

    $IQR = \text{Maximum Value} - \text{Minimum Value}$

    $IQR = Q_3 + Q_1$

    $IQR = Q_2 - Q_1$

    $IQR = Q_3 - Q_1$

24. If the Lower Quartile ($Q_1$) is $22$ and the Upper Quartile ($Q_3$) is $38$, what is the Interquartile Range (IQR)?

    $14$

    $16$

    $12$

    $60$

25. Dataset A has an $IQR = 5$, and Dataset B has an $IQR = 15$. Which dataset shows greater variability in its middle $50\%$?

    Dataset A, because $5$ is smaller.

    They both show the same variability.

    The range must be known to compare them.

    Dataset B, because $15$ is larger.

26. A set of heights has $Q_1 = 60$ inches and $Q_3 = 70$ inches. What is the IQR?

    $130$ inches

    $10$ inches

    $15$ inches

    $5$ inches

27. If $Q_1 = 4.5$ and $Q_3 = 18.5$, calculate the IQR.

    $15$

    $14$

    $23$

    $13.5$

28. A dataset has a Range of $100$ and an IQR of $10$. What does this suggest about the data?

    The data is tightly clustered overall.

    The mean is much higher than the median.

    The data is clustered evenly from minimum to maximum.

    There are likely significant outliers far from the central $50\%$.

29. Consider the following dataset: $5, 10, 15, 20, 25, 30, 35$. Calculate the Range.

    $25$

    $30$

    $5$

    $35$

30. Using the dataset $5, 10, 15, 20, 25, 30, 35$, what is the Median ($Q_2$)?

    $25$

    $15$

    $20$

    $17.5$

31. Using the dataset $5, 10, 15, 20, 25, 30, 35$, what is the Lower Quartile ($Q_1$)?

    $12.5$

    $15$

    $10$

32. Using the dataset $5, 10, 15, 20, 25, 30, 35$, what is the Upper Quartile ($Q_3$)?

    $27.5$

    $30$

    $25$

33. Using the dataset $5, 10, 15, 20, 25, 30, 35$, calculate the Interquartile Range (IQR). (Hint: $Q_1=10, Q_3=30$)

    $25$

    $15$

    $20$

    $10$

34. A dataset is highly skewed (has many values clustered at one end). Which measure of variability is usually less affected by this skewness or by extreme outliers?

    The Range

    The Median

    The Interquartile Range (IQR)

    The Mean

35. Which statement correctly pairs the measure of spread with what it describes?

    IQR measures the difference between the mean and the median.

    Range measures the distance between the maximum and minimum; IQR measures the spread of the central $50\%$.

    Range is always greater than the IQR.

    Range measures the middle $50\%$; IQR measures the whole dataset.

36. A group of students recorded the following scores on a math quiz: $12, 8, 15, 10, 14, 11, 9$. What is the median ($Q_2$) score for this dataset?

    $11$

    $9.5$

    $10$

    $12$

37. Six athletes measured their heights (in centimeters): $140, 155, 142, 160, 148, 150$. What is the range of their heights?

    $10$ cm

    $160$ cm

    $155$ cm

    $20$ cm

38. Eight students tracked their monthly phone usage (in hours). When ordered, the data is $4, 5, 6, 7, 9, 10, 12, 15$. What is the value of the first quartile ($Q_1$)?

    $6.5$ hours

    $5$ hours

    $7$ hours

    $5.5$ hours

39. Using the ordered phone usage data set ($4, 5, 6, 7, 9, 10, 12, 15$), what is the value of the third quartile ($Q_3$)?

    $10$ hours

    $11.5$ hours

    $11$ hours

    $12$ hours

40. Based on the dataset used for phone usage, where the first quartile ($Q_1$) is $5.5$ hours and the third quartile ($Q_3$) is $11$ hours, calculate the Interquartile Range (IQR).

    $16.5$ hours

    $4.5$ hours

    $5$ hours

    $5.5$ hours

41. A fitness tracker recorded the following daily steps (in thousands): $5, 8, 12, 6, 10, 15, 7, 9, 11$. What are the values for $Q_1$ and $Q_3$, respectively?

    $Q_1 = 6.5, Q_3 = 11$

    $Q_1 = 6.5, Q_3 = 11.5$

    $Q_1 = 6, Q_3 = 12$

    $Q_1 = 7, Q_3 = 11$

42. Using the daily steps dataset where $Q_1 = 6.5$ and $Q_3 = 11.5$ (in thousands of steps), calculate the Interquartile Range (IQR).

    $4.5$

    $5.5$

    $5$

    $4$

43. Dataset X has an Interquartile Range (IQR) of $8$, and Dataset Y has an IQR of $4$. Which statement correctly describes the variability of the middle $50\%$ of the data?

    Dataset X is more spread out than Dataset Y in the middle $50\%$.

    The range must be larger for Dataset Y.

    Both datasets have the same variability.

    Dataset X is less variable than Dataset Y in the middle $50\%$.

44. What is the correct sequence of steps required to calculate the Interquartile Range (IQR) for any given dataset?

    Order the data, find $Q_1$ and $Q_3$, find the median ($Q_2$).

    Order the data, find the minimum and maximum, subtract the values.

    Order the data, find the median ($Q_2$), find $Q_1$ and $Q_3$, then calculate $Q_3 - Q_1$.

    Find the median, find the range, calculate $Q_3 - Q_1$.

45. Ten students received the following test scores: $60, 75, 80, 85, 90, 90, 95, 100, 70, 65$. Calculate both the Range and the Interquartile Range (IQR).

    Range $= 45$; IQR $= 20$

    Range $= 35$; IQR $= 15$

    Range $= 40$; IQR $= 25$

    Range $= 40$; IQR $= 20$