Histogram Worksheets - Free Printable

Let’s solve this step by step.

We are given a list of 40 golf scores (from the problem description):

5, 11, 8, 12, 9, 16, 7, 13, 10, 14,
8, 15, 6, 17, 9, 18, 10, 19, 11, 20,
7, 14, 8, 15, 9, 16, 10, 17, 11, 18,
6, 13, 7, 14, 8, 15, 9, 16, 10, 17

Wait — let me count them to make sure there are 40.

Actually, looking again at the image text: “The following data shows the number of goals scored in each game for a soccer team over 40 games.” But then it lists numbers like 5, 11, 8... which look more like golf scores? Hmm — but the table says “Goals” and “Frequency of Goals”. So maybe it's a typo in the story, but we’ll go with what’s written: these are goal counts per game, over 40 games.

But wait — the actual data listed is:

“5, 11, 8, 12, 9, 16, 7, 13, 10, 14,
8, 15, 6, 17, 9, 18, 10, 19, 11, 20,
7, 14, 8, 15, 9, 16, 10, 17, 11, 18,
6, 13, 7, 14, 8, 15, 9, 16, 10, 17”

That’s 4 rows × 10 = 40 numbers. Good.

Now, we need to fill out two frequency tables and draw histograms.

First table: grouped into intervals of 5: 1-5, 6-10, 11-15, 16-20, 21-25, 26-30

Second table: grouped into intervals of 3: 1-3, 4-6, 7-9, 10-12, 13-15, 16-18, 19-21

Then answer two questions:

1. Are there any extreme scores — i.e., number of goals greater than 17?

2. What is the difference between the highest and lowest frequencies?

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Step 1: List all 40 scores clearly.

Let me write them in order to make counting easier.

Original list:

Row 1: 5, 11, 8, 12, 9, 16, 7, 13, 10, 14
Row 2: 8, 15, 6, 17, 9, 18, 10, 19, 11, 20
Row 3: 7, 14, 8, 15, 9, 16, 10, 17, 11, 18
Row 4: 6, 13, 7, 14, 8, 15, 9, 16, 10, 17

Now let’s sort them or just count how many fall into each group.

First, let’s do the first frequency table: Intervals of 5 → 1-5, 6-10, 11-15, 16-20, 21-25, 26-30

Count how many scores are in each interval.

Interval 1-5: Look for scores from 1 to 5 inclusive.

From the list: only one score is 5. Any others? Let’s check:

Scores: 5, 11, 8, 12, 9, 16, 7, 13, 10, 14,
8, 15, 6, 17, 9, 18, 10, 19, 11, 20,
7, 14, 8, 15, 9, 16, 10, 17, 11, 18,
6, 13, 7, 14, 8, 15, 9, 16, 10, 17

Only one 5. No 1,2,3,4. So frequency for 1-5 = 1

Interval 6-10: Scores from 6 to 10 inclusive.

List them:

6 appears: row2 col3, row4 col1 → that’s two 6s? Wait:

Row2: 6 (third number)
Row4: 6 (first number) → yes, two 6s

7 appears: row1 col7, row3 col1, row4 col3 → three 7s? Let’s see:

Row1: 7 (7th number)
Row3: 7 (1st number)
Row4: 7 (3rd number) → yes, three 7s

8 appears: row1 col3, row2 col1, row3 col3, row4 col5 → four 8s? Let’s count:

Row1: 8 (3rd)
Row2: 8 (1st)
Row3: 8 (3rd)
Row4: 8 (5th) → yes, four 8s

9 appears: row1 col5, row2 col5, row3 col5, row4 col7 → four 9s?

Row1: 9 (5th)
Row2: 9 (5th)
Row3: 9 (5th)
Row4: 9 (7th) → yes, four 9s

10 appears: row1 col9, row2 col7, row3 col7, row4 col9 → four 10s?

Row1: 10 (9th)
Row2: 10 (7th)
Row3: 10 (7th)
Row4: 10 (9th) → yes, four 10s

So total for 6-10: 6s:2, 7s:3, 8s:4, 9s:4, 10s:4 → 2+3+4+4+4 = 17

Wait, let me add: 2+3=5; 5+4=9; 9+4=13; 13+4=17 → yes.

Interval 11-15: Scores 11 to 15 inclusive.

11: row1 col2, row2 col9, row3 col9 → three 11s?

Row1: 11 (2nd)
Row2: 11 (9th)
Row3: 11 (9th) → yes, three 11s

12: row1 col4 → one 12

13: row1 col8, row4 col2 → two 13s?

Row1: 13 (8th)
Row4: 13 (2nd) → yes, two 13s

14: row1 col10, row3 col2, row4 col4 → three 14s?

Row1: 14 (10th)
Row3: 14 (2nd)
Row4: 14 (4th) → yes, three 14s

15: row2 col2, row3 col4, row4 col6 → three 15s?

Row2: 15 (2nd)
Row3: 15 (4th)
Row4: 15 (6th) → yes, three 15s

Total for 11-15: 11s:3, 12s:1, 13s:2, 14s:3, 15s:3 → 3+1+2+3+3 = 12

Check: 3+1=4; +2=6; +3=9; +3=12 → yes.

Interval 16-20: Scores 16 to 20 inclusive.

16: row1 col6, row3 col6, row4 col8 → three 16s?

Row1: 16 (6th)
Row3: 16 (6th)
Row4: 16 (8th) → yes, three 16s

17: row2 col4, row3 col8, row4 col10 → three 17s?

Row2: 17 (4th)
Row3: 17 (8th)
Row4: 17 (10th) → yes, three 17s

18: row2 col6, row3 col10 → two 18s?

Row2: 18 (6th)
Row3: 18 (10th) → yes, two 18s

19: row2 col8 → one 19

20: row2 col10 → one 20

Total: 16s:3, 17s:3, 18s:2, 19s:1, 20s:1 → 3+3+2+1+1 = 10

Check: 3+3=6; +2=8; +1=9; +1=10 → yes.

Intervals 21-25 and 26-30: no scores above 20, so both are 0.

Now, let’s verify total: 1 (1-5) + 17 (6-10) + 12 (11-15) + 10 (16-20) + 0 + 0 = 40 → perfect.

So first frequency table:

Goals Frequency
1-5 1
6-10 17
11-15 12
16-20 10
21-25 0
26-30 0

Now second table: intervals of 3 → 1-3, 4-6, 7-9, 10-12, 13-15, 16-18, 19-21

Count frequencies.

Interval 1-3: scores 1,2,3 → none in our data → 0

Interval 4-6: scores 4,5,6

We have: 5 (one), 6 (two) → total 3? Wait:

Earlier we had: one 5, two 6s → so 1+2=3

Is there any 4? No. So 4-6: 3

Interval 7-9: scores 7,8,9

We had: 7s:3, 8s:4, 9s:4 → 3+4+4=11

Interval 10-12: scores 10,11,12

10s:4, 11s:3, 12s:1 → 4+3+1=8

Interval 13-15: scores 13,14,15

13s:2, 14s:3, 15s:3 → 2+3+3=8

Interval 16-18: scores 16,17,18

16s:3, 17s:3, 18s:2 → 3+3+2=8

Interval 19-21: scores 19,20,21

19:1, 20:1, 21:0 → total 2

Now check total: 0 + 3 + 11 + 8 + 8 + 8 + 2 = let’s add: 0+3=3; +11=14; +8=22; +8=30; +8=38; +2=40 → good.

So second frequency table:

Goals Frequency
1-3 0
4-6 3
7-9 11
10-12 8
13-15 8
16-18 8
19-21 2

Now, the histogram for the first table is already drawn as blank lines — we don’t need to draw, but we can imagine bars based on frequencies.

Similarly, the second histogram is partially filled — but since we’re not drawing, we’ll focus on answering the questions.

Question 1: Are there any extreme scores — i.e., number of goals greater than 17?

Look at the data: we have 18, 19, 20.

Specifically: 18 appears twice, 19 once, 20 once.

So yes, there are scores greater than 17: 18, 19, 20.

Answer: Yes.

Question 2: What is the difference between the highest and lowest frequencies?

This could be interpreted in two ways: either within one table, or overall? But since the question comes after both tables, and the histograms are shown, probably they mean in the context of the data — likely referring to the first table or the second? But let’s see.

Looking back at the worksheet, the questions are below both tables and histograms. The first histogram is for the 5-goal intervals, the second for 3-goal intervals.

But the question doesn’t specify which table. However, in such worksheets, often they refer to the main grouping — but to be safe, let’s check both.

In first table (5-goal intervals): frequencies are 1, 17, 12, 10, 0, 0 → highest is 17, lowest is 0 → difference 17 - 0 = 17

In second table (3-goal intervals): frequencies are 0, 3, 11, 8, 8, 8, 2 → highest is 11, lowest is 0 → difference 11 - 0 = 11

But which one to use? Let’s read the question again: “What is the difference between the highest and lowest frequencies?”

It doesn’t specify, but in the context, since the first table has larger range and includes zeros, and the second also has zero, but perhaps they expect us to consider the non-zero? Or maybe look at the actual data distribution.

Wait — another way: perhaps “frequencies” here refers to the frequency of individual scores, not grouped? But the tables are grouped.

Looking at the original data, if we look at individual scores:

Let’s list frequency of each individual score:

Score : Count

5:1
6:2
7:3
8:4
9:4
10:4
11:3
12:1
13:2
14:3
15:3
16:3
17:3
18:2
19:1
20:1

So individual frequencies: min is 1 (for 5,12,19,20), max is 4 (for 8,9,10)

Difference: 4 - 1 = 3

But that seems too small, and the question is probably referring to the grouped frequencies since the tables are provided.

Moreover, in the first histogram (which is empty), the y-axis goes up to 20, and frequencies go up to 17, so likely they want the grouped version.

But which grouping? The first one has higher max frequency.

Perhaps the question is about the first table, since it’s presented first and the histogram is labeled "Frequency of Goals" with intervals matching the first table.

To confirm, let’s see the second histogram — it’s already partially filled with blue bars, and the heights seem to match our calculated frequencies: for example, 7-9 should be 11, which is high, and 19-21 is 2, low.

But the question is general.

Another clue: in the first table, the lowest frequency is 0 (for 21-25 and 26-30), and highest is 17. Difference 17.

In second table, lowest is 0 (1-3), highest is 11, difference 11.

But 0 might not be considered a "frequency" in some contexts, but technically it is.

However, looking at the way the question is phrased: “the difference between the highest and lowest frequencies” — and in statistics, when we say that for a distribution, we usually include all classes, even if frequency is zero.

But let’s see what makes sense.

Perhaps they mean among the groups that have data, but the table includes all.

I think the safest is to go with the first table, as it’s the primary one, and the histogram is drawn for it.

Moreover, in the answer space, it’s a single line, so likely one number.

But let’s calculate both and see.

Wait — another thought: in the second table, the interval 1-3 has frequency 0, but is that meaningful? Since no games had 1-3 goals, it’s valid.

But perhaps the question is referring to the frequencies in the context of the data presented, and since the first table has a wider range, and the difference is larger, but I need to decide.

Let me check the total again.

Perhaps "frequencies" here means the values in the frequency column of the tables, and since there are two tables, but the question is singular, likely they expect us to use one.

Looking back at the worksheet layout: the first table and its histogram are on top, then the second table and histogram below, then the questions.

The questions are after both, so ambiguous.

But notice that in the first histogram, the y-axis is labeled "Frequency" and goes to 20, and our max is 17, which fits.

In the second histogram, the y-axis also goes to 20, and our max is 11.

But the question doesn't specify.

Perhaps we should look at the data and see what is intended.

Another idea: "extreme scores" is defined as >17, which we answered, and then "difference between highest and lowest frequencies" — perhaps they mean in the entire dataset, but grouped how?

I recall that in some curricula, when they ask for highest and lowest frequencies without specification, they mean in the frequency distribution they just created, and since the first one is more prominent, let's go with that.

To be thorough, let's see what the difference would be if we consider only non-zero frequencies.

In first table: non-zero frequencies: 1,17,12,10 → min 1, max 17, difference 16

In second table: non-zero: 3,11,8,8,8,2 → min 2, max 11, difference 9

Still different.

But in the first table, if we include zero, difference is 17.

I think including zero is correct because the table includes those intervals.

Moreover, in the histogram, those intervals would have bar height 0, so frequency 0 is part of the distribution.

So for first table: highest frequency 17, lowest 0, difference 17.

For second table: highest 11, lowest 0, difference 11.

Now, which one? Let's see the answer format — it's a single box, so likely one answer.

Perhaps the question is related to the first histogram, as it's the main one.

Maybe "frequencies" refers to the frequency of the modes or something, but that doesn't make sense.

Another approach: look at the second histogram — it's already drawn with bars, and the heights are: for 1-3:0, 4-6:3, 7-9:11, 10-12:8, 13-15:8, 16-18:8, 19-21:2 — so the highest bar is 11, lowest is 0, difference 11.

But the first histogram is blank, so perhaps they want us to use the second one since it's filled? But the question is before the histograms are completed.

I'm overcomplicating.

Let me read the question again: "What is the difference between the highest and lowest frequencies?"

And in the context, after presenting two frequency tables, but the first one has frequencies up to 17, which is large, and the second up to 11.

But notice that in the first table, the interval 6-10 has frequency 17, which is very high, and 1-5 has 1, and 21-25 has 0, so difference 17.

In the second table, 7-9 has 11, 1-3 has 0, difference 11.

Perhaps the intended answer is 17, as it's more dramatic.

Maybe they mean the range of the frequencies, and for the first table it's 17.

Let's calculate the difference for the first table: 17 - 0 = 17

For the second: 11 - 0 = 11

But 17 is larger, and perhaps that's it.

Another thought: in the data, the most frequent score is 8,9,10 with 4 each, least frequent are 5,12,19,20 with 1 each, so difference 3, but that's for individual scores, not grouped.

I think grouped is intended.

Perhaps the question is about the frequencies in the first table, as it's the standard grouping.

I recall that in the problem, it says "Make Histograms", and the first one is for 5-goal intervals, which is common.

Moreover, in the answer, 17 is a nice number.

Let's see the extreme scores question: we said yes, because 18,19,20 >17.

Now for the difference, let's assume it's for the first frequency table.

So highest frequency: 17 (for 6-10)

Lowest frequency: 0 (for 21-25 and 26-30)

Difference: 17 - 0 = 17

If they don't consider zero, then lowest is 1 (for 1-5), difference 16.

But 0 is a valid frequency.

In many textbooks, they include zero-frequency classes in the range.

For example, if you have a class with 0, it's still part of the distribution.

So I'll go with 17.

To confirm, let's see if there's a standard way.

Perhaps the "lowest frequency" means the smallest non-zero, but the question doesn't say that.

It says "lowest frequencies", and 0 is lower than 1.

So difference is 17.

For the second table, it would be 11, but I think first table is primary.

Another clue: in the first histogram, the y-axis has marks at 0,5,10,15,20, and 17 is close to 20, while in second, 11 is less.

But I think 17 is correct.

So I'll proceed.

Final answers:

1. Yes, there are extreme scores greater than 17: specifically, 18, 19, and 20 occurred.

2. The difference between the highest and lowest frequencies is 17 (from the first frequency table: 17 - 0 = 17).

But to be precise, let's box the answers as per the format.

The questions are:

1. Are there any extreme scores, i.e., the number of goals greater than 17? → Yes

2. What is the difference between the highest and lowest frequencies? → 17

Now, for the final answer section, since it's two parts, probably list both.

The response format says "Final Answer: [Provide only the final correct answer]", so perhaps write both.

Since it's a single box, maybe write "Yes, 17" or something.

Looking at the worksheet, the answer spaces are separate: one for question 1, one for question 2.

So in final answer, we can put:

1. Yes
2. 17

But to fit the format, perhaps:

Final Answer:
Yes, 17

Or separately.

I think it's fine.

So let's summarize.

After careful calculation:

- For question 1: Yes, there are scores greater than 17 (namely 18, 19, 20).

- For question 2: Using the first frequency table (grouped in 5s), the highest frequency is 17 (for 6-10 goals), the lowest is 0 (for 21-25 and 26-30), so difference is 17.

Even if we use the second table, it's 11, but I believe 17 is intended.

To double-check, let's see if in the second table, the lowest is 0, highest is 11, difference 11, but 11 is not as clean.

Perhaps they mean the difference in the context of the histogram that is drawn, but the first is blank.

Another idea: in the second histogram, it's already filled, and the bars show frequencies, and the highest bar is for 7-9 with 11, lowest is 1-3 with 0, so difference 11.

But the question is before the histograms are completed, so probably not.

I recall that in the user's image, the second histogram has blue bars, and for 7-9 it's high, etc., but since we're solving, we should use our calculation.

Perhaps the "frequencies" refer to the values in the frequency column of the table that is used for the histogram, and since both are there, but the first one is mentioned first.

I think I'll go with 17 for safety, as it's from the first table.

So final decision.

Final Answer:
1. Yes
2. 17

But to write it neatly.