Histogram and frequency analysis in Excel - Cell-by-Cell Formula Trace

Sample Data

This data shows student test scores in column A and bin limits in column B for grouping scores.

Cell	Value
A1	Scores
A2	55
A3	67
A4	45
A5	70
A6	89
A7	90
A8	72
A9	60
A10	85
B1	Bins
B2	50
B3	60
B4	70
B5	80
B6	90
C1	Frequency

Formula Trace

=FREQUENCY(A2:A10, B2:B6)

Step 1: A2:A10

Step 2: B2:B6

Step 3: FREQUENCY([55,67,45,70,89,90,72,60,85], [50,60,70,80,90])

Cell Reference Map

1

↓

2

↓

3

↓

4

↓

5

The formula uses scores from A2:A10 and bins from B2:B6 to calculate frequency counts.

Result

    A      B      C
1 Scores  Bins  Frequency
2  55     50      1
3  67     60      2
4  45     70      2
5  70     80      1
6  89     90      2
7  90             1
8  72
9  60
10 85

Column C shows how many scores fall into each bin range defined in column B.

Sheet Trace Quiz - 3 Questions

How many scores are less than or equal to 50?

A 0

B 2

C 1

D 3

Key Result

FREQUENCY(data_array, bins_array) returns counts of values in data_array grouped by bins_array limits.

Practice

1. What does the FREQUENCY function in Excel do when given a data array and bins array?

easy

A. Finds the maximum value in each bin

B. Sorts the data array in ascending order

C. Calculates the average of numbers in each bin

D. Counts how many data points fall into each bin range

Solution

1. Step 1: Understand FREQUENCY function purpose

   The FREQUENCY function counts how many values from the data array fall into each bin range defined by the bins array.

2. Step 2: Analyze the function output

   It returns an array where each element shows the count of data points within each bin interval.

3. Final Answer:

   Counts how many data points fall into each bin range -> Option D

4. Quick Check:

   FREQUENCY counts data per bin [OK]

Hint: FREQUENCY counts items per bin, not sorts or averages [OK]

Common Mistakes:

• Thinking FREQUENCY sorts data
• Assuming FREQUENCY calculates averages
• Confusing FREQUENCY with MAX or MIN functions

2. Which of the following is the correct way to enter the FREQUENCY function as an array formula in Excel for data in A2:A10 and bins in B2:B5?

easy

A. =FREQUENCY(A2:A10, B2:B5)

B. =FREQUENCY(A2:A10; B2:B5)

C. =FREQUENCY(A2:A10 B2:B5)

D. =FREQUENCY(A2:A10, B2:B5) entered normally

Solution

1. Step 1: Check FREQUENCY function syntax

   The correct syntax uses a comma to separate arguments: =FREQUENCY(data_array, bins_array).

2. Step 2: Understand array formula entry

   In modern Excel, pressing Enter is enough; older versions require Ctrl+Shift+Enter, but syntax remains the same.

3. Final Answer:

   =FREQUENCY(A2:A10, B2:B5) -> Option A

4. Quick Check:

   Correct syntax uses comma and proper ranges [OK]

Hint: Use commas between arguments; no semicolons in standard Excel [OK]

Common Mistakes:

• Using semicolons instead of commas
• Missing comma between arguments
• Entering formula without array selection in old Excel

3. Given data in cells A2:A7 as {2, 5, 7, 3, 8, 10} and bins in B2:B4 as {3, 6, 9}, what is the result of =FREQUENCY(A2:A7, B2:B4) entered as an array formula?

medium

A. {1, 3, 1, 1}

B. {1, 2, 2, 1}

C. {2, 1, 2, 1}

D. {3, 1, 1, 1}

Solution

1. Step 1: Identify bins and count data per bin

   Bins are 3, 6, 9. Count how many data points fall ≤3, >3 and ≤6, >6 and ≤9, and >9.

2. Step 2: Count data points in each bin

   Values: 2 (≤3), 3 (≤3), 5 (>3 ≤6), 7 (>6 ≤9), 8 (>6 ≤9), 10 (>9). Counts: ≤3 -> 2 values (2,3), >3 ≤6 -> 1 value (5), >6 ≤9 -> 2 values (7,8), >9 -> 1 value (10).

3. Final Answer:

   {2, 1, 2, 1} -> Option C

4. Quick Check:

   Count per bin matches {2,1,2,1} [OK]

Hint: Count data points in each bin range carefully [OK]

Common Mistakes:

• Miscounting values on bin edges
• Ignoring the last bin for values above highest bin
• Confusing bin intervals as inclusive/exclusive

4. You entered =FREQUENCY(A2:A10, B2:B5) but the result shows only one number instead of an array. What is the likely cause?

medium

A. You pressed Enter instead of Ctrl+Shift+Enter in an older Excel version

B. The bins array is empty

C. The data array contains text values

D. The formula syntax is incorrect

Solution

1. Step 1: Understand array formula behavior in older Excel

   In Excel versions before dynamic arrays, FREQUENCY must be entered as an array formula using Ctrl+Shift+Enter to return multiple values.

2. Step 2: Identify cause of single value output

   If only Enter is pressed, Excel returns only the first element of the frequency array, showing one number.

3. Final Answer:

   You pressed Enter instead of Ctrl+Shift+Enter in an older Excel version -> Option A

4. Quick Check:

   Old Excel needs Ctrl+Shift+Enter for array formulas [OK]

Hint: Use Ctrl+Shift+Enter for array formulas in old Excel [OK]

Common Mistakes:

• Not entering as array formula in old Excel
• Assuming single number means formula error
• Ignoring Excel version differences

5. You have sales data in A2:A20 and want to create a histogram with bins B2:B6. You want to show the frequency counts in C2:C7. Which formula should you enter in C2:C7 to get correct counts, and how should you enter it?

hard

A. Enter =COUNTIF(A2:A20, "<="&B2) in C2 and drag down

B. Select C2:C7, enter =FREQUENCY(A2:A20, B2:B6), then press Ctrl+Shift+Enter

C. Enter =FREQUENCY(A2:A20, B2:B6) in C2 and press Enter

D. Select C2:C6, enter =FREQUENCY(A2:A20, B2:B6), then press Ctrl+Shift+Enter

Solution

1. Step 1: Determine output size for FREQUENCY

   FREQUENCY returns an array with one more element than bins, so for 5 bins, output needs 6 cells (C2:C7).

2. Step 2: Enter FREQUENCY as array formula

   Select C2:C7, type =FREQUENCY(A2:A20, B2:B6), then press Ctrl+Shift+Enter (in older Excel) to fill all cells with counts.

3. Final Answer:

   Select C2:C7, enter =FREQUENCY(A2:A20, B2:B6), then press Ctrl+Shift+Enter -> Option B

4. Quick Check:

   Output range size = bins + 1, enter as array formula [OK]

Hint: Output range must be bins count + 1, enter as array formula [OK]

Common Mistakes:

• Selecting wrong output range size
• Not entering as array formula in old Excel
• Using COUNTIF which counts differently