Frequency Table Generator worksheet

1. Modal class (most values): 16–23 (4 values)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 16, max = 90}$

2. Use the class width you chose

   $\mathrm{width}$$=8$

3. Make 10 classes of width 8. Each stops just before the next one starts, so every value fits in exactly one

   $\text{16–23, 24–31, 32–39, 40–47, 48–55, 56–63, 64–71, 72–79, …}$

4. Tally how many values fall in each class

   $\text{16–23: 4, 24–31: 2, 32–39: 3, 40–47: 2, 48–55: 1, 56–63: 1, 64–71: 1, 72–79: 0, …}$

5. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{4}{15}$$=\mathrm{26.6667\%}$

6. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{4, 6, 9, 11, 12, 13, 14, 14, …, 15}$

7. The most frequent class is

   $\text{16–23 (4 values)}$

2. Most frequent value (mode): 18 and 45 (2 values each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 13, max = 65}$

2. Count how many times each distinct value appears

   $\text{13: 1, 18: 2, 26: 1, 29: 1, 33: 1, 35: 1, 36: 1, 38: 1, 40: 1, 45: 2, …}$

3. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{1}{15}$$=\mathrm{6.6667\%}$

4. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{1, 3, 4, 5, 6, 7, 8, 9, …, 15}$

5. The most frequent valuees tie

   $\text{18 and 45 (2 values each)}$

3. Most frequent value (mode): 38 and 52 (2 values each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 12, max = 54}$

2. Count how many times each distinct value appears

   $\text{12: 1, 16: 1, 18: 1, 24: 1, 28: 1, 32: 1, 36: 1, 38: 2, 40: 1, 45: 1, …}$

3. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{1}{15}$$=\mathrm{6.6667\%}$

4. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{1, 2, 3, 4, 5, 6, 7, 9, …, 15}$

5. The most frequent valuees tie

   $\text{38 and 52 (2 values each)}$

4. Most frequent value (mode): 26 and 50 (2 values each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 13, max = 70}$

2. Count how many times each distinct value appears

   $\text{13: 1, 18: 1, 22: 1, 26: 2, 28: 1, 32: 1, 34: 1, 36: 1, 40: 1, 45: 1, …}$

3. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{1}{15}$$=\mathrm{6.6667\%}$

4. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{1, 2, 3, 5, 6, 7, 8, 9, …, 15}$

5. The most frequent valuees tie

   $\text{26 and 50 (2 values each)}$

5. Most frequent value (mode): 12 and 15 and 22 and 27 and 31 and 33 and 35 and 38 and 41 and 44 and 45 and 47 and 52 and 58 and 63 (1 value each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 12, max = 63}$

2. Count how many times each distinct value appears

   $\text{12: 1, 15: 1, 22: 1, 27: 1, 31: 1, 33: 1, 35: 1, 38: 1, 41: 1, 44: 1, …}$

3. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{1}{15}$$=\mathrm{6.6667\%}$

4. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{1, 2, 3, 4, 5, 6, 7, 8, …, 15}$

5. The most frequent valuees tie

   $\text{12 and 15 and 22 and 27 and 31 and 33 and 35 and 38 and 41 and 44 and 45 and 47 and 52 and 58 and 63 (1 value each)}$

6. Modal class (most values): 21–29 (4 values)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 12, max = 65}$

2. Find the range, the span the classes must cover: the largest value minus the start of the first class

   $\mathrm{range}$$=65-12$$=53$

3. Split that range into 6 equal classes

   $\frac{53}{6}$$=8.833333$

4. Round up to match the data's decimal places (1)

   $\mathrm{width}$$=9$

5. Make 6 classes of width 9. Each stops just before the next one starts, so every value fits in exactly one

   $\text{12–20, 21–29, 30–38, 39–47, 48–56, 57–65}$

6. Tally how many values fall in each class

   $\text{12–20: 2, 21–29: 4, 30–38: 1, 39–47: 3, 48–56: 2, 57–65: 3}$

7. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{2}{15}$$=\mathrm{13.3333\%}$

8. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{2, 6, 7, 10, 12, 15}$

9. The most frequent class is

   $\text{21–29 (4 values)}$

7. Most frequent value (mode): 28 and 38 and 46 and 55 (2 values each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 8, max = 55}$

2. Count how many times each distinct value appears

   $\text{8: 1, 14: 1, 26: 1, 28: 2, 34: 1, 38: 2, 40: 1, 44: 1, 46: 2, 50: 1, …}$

3. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{1}{15}$$=\mathrm{6.6667\%}$

4. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{1, 2, 3, 5, 6, 8, 9, 10, …, 15}$

5. The most frequent valuees tie

   $\text{28 and 38 and 46 and 55 (2 values each)}$

8. Modal class (most values): 21–30 and 31–40 and 41–50 (3 values each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 11, max = 65}$

2. Find the range, the span the classes must cover: the largest value minus the start of the first class

   $\mathrm{range}$$=65-11$$=54$

3. Split that range into 6 equal classes

   $\frac{54}{6}$$=9$

4. Round up to match the data's decimal places (1). The division came out exact, so add one more unit to keep the largest value inside the last class

   $\mathrm{width}$$=10$

5. Make 6 classes of width 10. Each stops just before the next one starts, so every value fits in exactly one

   $\text{11–20, 21–30, 31–40, 41–50, 51–60, 61–70}$

6. Tally how many values fall in each class

   $\text{11–20: 2, 21–30: 3, 31–40: 3, 41–50: 3, 51–60: 2, 61–70: 2}$

7. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{2}{15}$$=\mathrm{13.3333\%}$

8. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{2, 5, 8, 11, 13, 15}$

9. The most frequent classes tie

   $\text{21–30 and 31–40 and 41–50 (3 values each)}$

9. Most frequent value (mode): 11 and 14 and 20 and 24 and 28 and 29 and 30 and 34 and 36 and 45 and 49 and 58 and 60 and 65 and 85 (1 value each)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 11, max = 85}$

2. Count how many times each distinct value appears

   $\text{11: 1, 14: 1, 20: 1, 24: 1, 28: 1, 29: 1, 30: 1, 34: 1, 36: 1, 45: 1, …}$

3. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{1}{15}$$=\mathrm{6.6667\%}$

4. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{1, 2, 3, 4, 5, 6, 7, 8, …, 15}$

5. The most frequent valuees tie

   $\text{11 and 14 and 20 and 24 and 28 and 29 and 30 and 34 and 36 and 45 and 49 and 58 and 60 and 65 and 85 (1 value each)}$

10. Modal class (most values): 35–55 (8 values)

1. Sort the 15 values (n) and note the smallest and largest, since the classes must cover both

   $\text{n = 15, min = 14, max = 75}$

2. Find the range, the span the classes must cover: the largest value minus the start of the first class

   $\mathrm{range}$$=75-14$$=61$

3. Split that range into 3 equal classes

   $\frac{61}{3}$$=20.333333$

4. Round up to match the data's decimal places (1)

   $\mathrm{width}$$=21$

5. Make 3 classes of width 21. Each stops just before the next one starts, so every value fits in exactly one

   $\text{14–34, 35–55, 56–76}$

6. Tally how many values fall in each class

   $\text{14–34: 5, 35–55: 8, 56–76: 2}$

7. Find each class's relative frequency, its share of all the values. Here's the first class

   $\frac{5}{15}$$=\mathrm{33.3333\%}$

8. Keep a running total of the counts for the cumulative frequency. The last total equals n, the number of values

   $\text{5, 13, 15}$

9. The most frequent class is

   $\text{35–55 (8 values)}$