Histogram and frequency analysis in Excel - Practice Problems & Coding Challenges

Challenge - 5 Problems

📊 Formula Result

intermediate

Calculate frequency distribution using FREQUENCY function

Given the data values in cells A2:A11 and bins in cells B2:B6, which formula entered in C2 and confirmed with Ctrl+Shift+Enter will correctly calculate the frequency distribution?

Excel

Data: A2:A11 = {3, 7, 8, 5, 12, 14, 21, 13, 18, 20}
Bins: B2:B6 = {5, 10, 15, 20, 25}

A =FREQUENCY(A2:A11, B2:B6)

B =COUNTIFS(A2:A11, ">" & B2:B6)

C =COUNTIF(A2:A11, "<=" & B2:B6)

D =FREQUENCY(B2:B6, A2:A11)

💡 Hint

Remember FREQUENCY(data_array, bins_array) counts how many data points fall into each bin range.

The FREQUENCY function syntax is FREQUENCY(data_array, bins_array). Option A correctly uses data in A2:A11 and bins in B2:B6. Option A reverses the arguments, causing wrong output. Options C and D use COUNTIF(S) which do not produce frequency arrays for bins.

❓ Function Choice

intermediate

Choose the best function to create a histogram in Excel

You want to create a histogram that groups sales data into ranges and shows counts for each range. Which Excel function is best suited to calculate the counts for each bin?

A AVERAGEIFS

B VLOOKUP

C FREQUENCY

D SUMIFS

💡 Hint

Think about a function that counts how many values fall into specified ranges.

FREQUENCY is designed to count how many data points fall into each bin range, perfect for histograms. SUMIFS sums values, AVERAGEIFS calculates averages, and VLOOKUP searches for values, so they are not suitable here.

❓ data_analysis

advanced

Analyze frequency output array length

If you use the formula =FREQUENCY(A2:A10, B2:B5) in Excel, how many elements will the resulting frequency array contain?

Excel

Data range: A2:A10 (9 values)
Bins range: B2:B5 (4 values)

A 4

B 10

C 9

D 5

💡 Hint

The FREQUENCY function returns one more element than the number of bins.

The FREQUENCY function returns an array with length equal to the number of bins plus one. The extra element counts values above the highest bin. Here bins are 4, so output length is 5.

🎯 Scenario

advanced

Identify the error in histogram frequency calculation

You entered the formula =FREQUENCY(A2:A20, B2:B10) in cell C2 and pressed Enter. The output shows a single number instead of an array of counts. What is the most likely reason?

A You forgot to press Ctrl+Shift+Enter to enter it as an array formula.

B The data range A2:A20 is empty.

C The bins range B2:B10 contains text values.

D The formula syntax is incorrect; FREQUENCY requires three arguments.

💡 Hint

Think about how array formulas behave in older Excel versions.

In Excel versions before dynamic arrays, FREQUENCY must be entered as an array formula with Ctrl+Shift+Enter to output multiple values. Pressing Enter alone returns only the first element.

📊 Formula Result

expert

Determine the frequency output for mixed data and bins

Given the data in A2:A8: {2, 5, 7, 10, 12, 15, 20} and bins in B2:B4: {5, 10, 15}, what is the output array of =FREQUENCY(A2:A8, B2:B4)?

Excel

Data: 2, 5, 7, 10, 12, 15, 20
Bins: 5, 10, 15

A {2, 3, 1, 1}

B {2, 2, 2, 1}

C {1, 2, 2, 2}

D {3, 2, 1, 1}

💡 Hint

Count how many data points fall into each bin range: <=5, >5 and <=10, >10 and <=15, >15.

Bins: 5, 10, 15 create ranges: - <=5: values 2,5 → 2 - >5 and <=10: values 7,10 → 2 - >10 and <=15: values 12,15 → 2 - >15: value 20 → 1 So output is {2, 2, 2, 1}.

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