Report Number of Observations - 6th Grade Math

1. Identify the number of observations in $\{4, 4, 7, 9, 9, 9\}$.

   $n = 6$. Count all values including duplicates.

2. What is the number of observations in the data set $\{100, 90, 80, 70, 60, 50, 40, 30\}$?

   $8$ observations. Large numbers count the same as small ones - one per value.

3. Identify the number of observations in the data set: $4, 7, 7, 9, 10$.

   $n = 5$. Count each value: there are 5 numbers total.

4. Identify the number of observations in this frequency table: values $1,2,3$ with frequencies $2,5,1$.

   $8$ observations. Sum all frequencies: $2 + 5 + 1 = 8$ total observations.

5. What is the number of observations in the data set $\{2, 4, 6, 8, 10, 12, 14, 16\}$?

   $n = 8$. Count each term in the sequence.

6. Identify the number of observations in the list: $20, 18, 19, 20, 17, 18, 20$.

   $n = 7$. Count each number in the list.

7. What is the number of observations in the data set $\{1.5, 2.0, 2.5, 3.0\}$?

   $n = 4$. Decimals count as individual observations.

8. What is the number of observations in the data set $\{0, -1, -1, 3, 5\}$?

   $5$ observations. Count all values, including negatives and duplicates.

9. What is the number of observations if $6$ students each report $1$ height measurement?

   $6$ observations. Each student's measurement is one observation.

10. What is the number of observations in the data set $\{2, 2, 2, 2, 2, 2\}$?

    $6$ observations. Repeated values each count as separate observations.

11. What is the number of observations if $4$ students each report $3$ test scores?

    $12$ observations. Multiply students by scores per student: $4 \times 3 = 12$.

12. Which statement is correct: repeats in $2, 2, 3$ count as $1$ observation or $3$ observations?

    Repeats count; the set has $n = 3$ observations. Each occurrence counts separately, not just unique values.

13. What is the number of observations in the data set $\{\frac{1}{2}, \frac{1}{2}, \frac{3}{4}\}$?

    $n = 3$. Fractions are counted like any other values.

14. What is $n$ if a frequency table has frequencies $2, 0, 5, 3$?

    $n = 10$. Add all frequencies: $2 + 0 + 5 + 3 = 10$.

15. What is the number of observations in a frequency table with counts $3, 4, 1$?

    $n = 8$. Sum all frequencies: $3 + 4 + 1 = 8$.

16. What is the number of observations in a dot plot with counts $3$ at $1$, $2$ at $2$, and $4$ at $3$?

    $9$ observations. Add all dot counts: $3 + 2 + 4 = 9$ observations.

17. What is the number of observations in the data set $\{12\}$?

    $1$ observation. Even a single value counts as one observation.

18. What is the number of observations in the data set $\{1.5, 2.0, 2.5, 3.0\}$?

    $4$ observations. Decimal values count the same as whole numbers.

19. What is the number of observations in the ordered list $1, 2, 3, 4, 5, 6, 7$?

    $n = 7$. Count each number in the ordered sequence.

20. What is $n$ if the sum of frequencies in a table is $25$?

    $n = 25$. Total observations equals sum of all frequencies.

21. What is the number of observations in the data set $\{4, 7, 7, 10\}$?

    $4$ observations. Count each value in the set, including duplicates.

22. Find the number of observations when a bar graph shows category counts of $5$, $7$, $2$, and $6$.

    $20$ observations. Add all bar heights: $5 + 7 + 2 + 6 = 20$ observations.

23. What is the number of observations if a data set has frequencies $4, 6, 3$ across its categories?

    $13$ observations. Sum frequencies across categories: $4 + 6 + 3 = 13$.

24. What does the phrase "number of observations" mean in a data set?

    The total count of data values in the set. Each value counts as one observation, regardless of repetition.

25. What is the number of observations in the data set $\{\frac{1}{2}, \frac{1}{2}, \frac{3}{4}\}$?

    $3$ observations. Fractions count as observations just like other numbers.

26. Find the number of observations if $5$ students each recorded $3$ measurements.

    $n = 15$. Multiply: $5 \times 3 = 15$ total measurements.

27. Identify the number of observations shown by the dot plot (each dot is one value).

    $n = 9$. Count each dot as one observation.

28. What is the number of observations in the data set $\{3, 5, 7, 9, 11, 13, 15\}$?

    $7$ observations. Count each value in the set to find total observations.

29. What is the number of observations in the data set: $\frac{1}{2}, \frac{3}{4}, \frac{3}{4}$?

    $n = 3$. Fractions count as individual observations.

30. Find $n$ for the data set $\{9, 1, 9, 1, 9, 1, 9, 1, 9\}$.

    $n = 9$. Count all values, not unique values.

31. What is the number of observations in the data set $\{12\}$?

    $n = 1$. A single value means one observation.

32. What is the number of observations when a value appears $8$ times in a list?

    $n = 8$. Each occurrence counts as one observation.

33. Identify the number of observations if the data are grouped and the class frequencies sum to $30$.

    $n = 30$. The sum of all class frequencies gives total observations.

34. Find and correct the error: "Data set $4, 6, 6$ has $n=2$ because there are $2$ different values."

    Correct: $n = 3$ (count all values, not distinct values). The error was counting unique values instead of all occurrences.

35. What must you do to report the number of observations from a frequency table?

    Add all frequencies to get the total count. Frequencies show how many times each value appears.

36. What is the symbol commonly used to represent the number of observations?

    $n$. Standard notation in statistics for sample size.

37. What is the number of observations in the data set $\{3, 5, 5, 8\}$?

    $n = 4$. Count each value: 3, 5, 5, 8 gives 4 total.

38. Identify the number of observations represented by this bar chart (sum of bar heights).

    $n = 14$. Add all bar heights to find total count.

39. What is the number of observations in the data set: $9$ (a single value only once)?

    $n = 1$. A single value appearing once means one observation.

40. What is the number of observations in the ordered list $[9, 8, 7, 6, 5]$?

    $5$ observations. Order doesn't matter; count all values in the list.

41. What is the number of observations in the data set: $1.2, 1.2, 1.5, 1.8$?

    $n = 4$. Decimals are counted like any other values.

42. What is the number of observations if $8$ people are measured on $2$ variables each (height and arm span)?

    $16$ observations. Total observations = people × measurements per person.

43. Which calculation finds $n$ from frequencies $f_1, f_2, \dots, f_k$?

    $n = f_1 + f_2 + \cdots + f_k$. Sum all frequency values to get total observations.

44. What is the number of observations in the data set: $100, 98, 97, 96, 95, 94, 93, 92$?

    $n = 8$. Count from first to last value.

45. What symbol is commonly used to represent the number of observations in a data set?

    $n$. Standard statistical notation for sample size or observation count.

46. What is the number of observations if a survey records $1$ response from each of $25$ people?

    $25$ observations. One response per person means observations equal people.

47. Identify the error: A student says $n = 3$ for $\{5, 5, 5, 5\}$. What is $n$?

    Incorrect; $n = 4$. Student counted unique values; count all four 5's.

48. What is $n$ if a bar graph has category counts $7$, $5$, and $8$?

    $n = 20$. Sum category counts: $7 + 5 + 8 = 20$.

49. What is the number of observations if the frequencies are $6$, $1$, and $8$?

    $n = 15$. Add frequencies: $6 + 1 + 8 = 15$.

50. What is the number of observations in the data set $\{-2, -1, 0, 1, 2\}$?

    $n = 5$. Count includes negative, zero, and positive values.

51. Which option correctly reports the number of observations for $\{4, 4, 6\}$: $2$ or $3$?

    $3$. Count values, not unique values; duplicates count separately.

52. Identify $n$ if a dot plot shows $4$ dots above $2$ and $6$ dots above $3$.

    $n = 10$. Total dots equals total observations: $4 + 6 = 10$.

53. Which option correctly reports the number of observations for $5, 5, 5, 6$: $n=2$ or $n=4$?

    $n = 4$. $n=4$ counts all values; $n=2$ incorrectly counts unique values only.

54. What is the number of observations in the data set $\{0, 0, 0, 0, 0\}$?

    $n = 5$. Count all values, even if they're identical.

55. What does the phrase "number of observations" mean in a data set?

    The total count of data values in the set. Each data point counts as one observation, regardless of value.

56. Identify the number of observations in the data set: $-3, 0, 2, 5, 8, 8$.

    $n = 6$. Count every value in the list from first to last.

57. Identify the number of observations in the data set: $12, 12, 12, 15$.

    $n = 4$. Count all values including duplicates.

58. Identify the number of observations in this frequency table by adding the frequencies.

    $n = 12$. Sum all frequency values to get total observations.

59. What is the number of observations if a survey collected $28$ responses and removed $3$ invalid ones?

    $n = 25$. Subtract invalid from total: $28 - 3 = 25$.

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