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Report Number of
Observations

Learn how to count and report the total number of data points in a data set: the foundation of every statistical summary.

6th Grade Math

What Is an Observation?

An observation is a single piece of data that you collect or measure. Every time you record a value, you have created one observation.

★ Example
If you measure the height of one student, that is 1 observation.
★ Example
If you record test scores for 25 students, you have 25 observations.

What Is a Data Set?

A data set is the complete collection of observations gathered from a survey, experiment, or measurement. The number of observations tells us how large the data set is.

5 8 3 9 2 7 6 Data Set 7 values = 7 observations

Why Does Counting Matter?

Before you can find the mean, median, or range of any data set, you first need to know how many values there are. The number of observations is the starting point for every statistical calculation.

Mean
Divide the sum by \( n \), the number of observations.
Median
Need \( n \) to find the middle position.
Sample Size
Tells us how reliable our results are.

The Core Rule

DATA SET 4 7 4 10 3 7 5 1 2 3 4 5 6 7
\( n = 7 \) observations

Notice that 4 appears twice and 7 appears twice. Repeated values still count as separate observations.

Repeats Still Count

A common source of confusion: even when a value shows up multiple times, each occurrence is its own observation.

DATA SET 5 5 5 8 12 3 separate observations (not 1)
\( n = 5 \) observations

Observation vs. Unique Value

It is important to distinguish between the number of observations (\( n \)) and the number of unique (distinct) values. They are not the same thing.

Observations (\( n \)) Unique Values
Definition Total count of all data points Count of different values
Data: 3, 5, 3, 7, 5 5 3 (which are 3, 5, 7)
Data: 2, 2, 2, 2 4 1 (which is 2)
Includes repeats? Yes No

Reading \( n \) from a Frequency Table

When data is presented in a frequency table, you find \( n \) by adding up all the frequencies.

Score Frequency 70 4 80 6 90 5 100 3
\( n = 4 + 6 + 5 + 3 = 18 \)

Reading \( n \) from a Dot Plot

On a dot plot, each dot is one observation. Count every dot above the number line to find \( n \).

1 2 3 4 5
Count all dots: \( n = 2 + 3 + 4 + 1 + 2 = 12 \)

How to Report the Number of Observations

1
Identify the data source. Is it a list, a frequency table, a dot plot, a bar graph, or a histogram?
2
Count every individual data value. If given a list, count each entry. If given a table or graph, add up all the frequencies.
3
Include repeats. A value that appears 4 times counts as 4 observations, not 1.
4
Write your answer. State: "There are \( n = \text{[your count]} \) observations."

Example 1: Counting a List

A teacher recorded quiz scores for her class:

85 92 78 85 90 67 88 95 85 Count each value: 1, 2, 3, 4, 5, 6, 7, 8, 9

Example 2: Frequency Table

Students were asked how many pets they own:

Number of Pets Frequency 0 5 1 8 2 7 3 4 4+ 2
\( n = 5 + 8 + 7 + 4 + 2 = 26 \)

Example 3: Bar Graph

A bar graph shows how students get to school. Read the height of each bar to find its frequency, then add them up.

0 5 10 15 20 12 Bus 8 Car 5 Walk 3 Bike Students

Common Mistakes

✕ Ignoring Repeats
Counting 3, 5, 3, 7 as \( n = 3 \) (only unique values) instead of \( n = 4 \).
✕ Counting Categories
In a frequency table with 5 rows, saying \( n = 5 \) instead of adding the frequencies.
✕ Skipping Zero
In data like {0, 3, 5, 0}, forgetting that 0 is still a valid observation. \( n = 4 \), not \( 2 \).

Summary: Finding \( n \)

Data Format How to Find \( n \) Example
Raw List Count every value in the list {4, 7, 4, 9} → \( n = 4 \)
Frequency Table Add all frequencies together 3 + 5 + 2 = 10 → \( n = 10 \)
Dot Plot Count every dot 15 dots total → \( n = 15 \)
Bar Graph Add the heights of all bars 8 + 6 + 4 = 18 → \( n = 18 \)
Histogram Add the frequencies of all bins 7 + 10 + 3 = 20 → \( n = 20 \)

Question 1 of 5

A data set contains the values: 12, 7, 9, 12, 15, 7, 12. How many observations are there?

Question 2 of 5

A frequency table has four rows with frequencies: 6, 9, 4, 11. What is the number of observations?

Question 3 of 5

A dot plot has the following dots above each value:
Value 2: 3 dots, Value 4: 5 dots, Value 6: 2 dots.
What is \( n \)?

Question 4 of 5

The data set is: 0, 0, 5, 3, 0, 8. What is the number of observations?

Question 5 of 5

A bar graph shows the favorite fruits of students. The bars have heights: Apples: 14, Bananas: 9, Grapes: 7, Oranges: 10. How many students were surveyed?