10.02 Frequency tables
Complete the frequency table below based on the following data set:
2,\, 5,\, 4,\, 5,\, 5,\, 5,\, 3,\, 4,\, 5,\, 5,\, 1,\, 3,\, 3,\, 3,\, 5,\, 2,\, 4,\, 1,\, 6,\, 5,\, 6,\, 3,\, 1,\, 1,\, 6
| \text{Score} | \text{Frequency} |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 |
Complete the following frequency tables:
| \text{Score } (x) | \text{Frequency } (f) | xf |
|---|---|---|
| 1 | 7 | |
| 2 | 4 | |
| 3 | 7 | |
| 4 | 8 | |
| 5 | 8 | |
| 6 | 8 |
| \text{Score} | \text{Frequency} | \text{Cumulative} \\\ \text{frequency} |
|---|---|---|
| 4 | 5 | |
| 5 | 8 | |
| 6 | 7 | |
| 7 | 7 | |
| 8 | 3 | |
| 9 | 7 |
Construct a cumulative frequency table for each of the following data sets:
3,\, 6,\, 4,\, 4,\, 7,\, 5,\, 5,\, 6,\, 2,\, 4,\, 6,\, 5,\, 5,\, 2,\, 3,\, 6,\, 5,\, 3,\, 5,\, 2,\, 5,\, 2,\, 5,\, 6,\, 7
5,\, 4,\, 7,\, 8,\, 6,\, 4,\, 9,\, 4,\, 4,\, 8,\, 8,\, 5,\, 6,\, 9,\, 4,\, 9,\, 8,\, 6,\, 6,\, 7,\, 4,\, 4,\, 7,\, 4,\, 8
State the mode of the following data set:
| \text{Score} | \text{Frequency} |
|---|---|
| 3 | 3 |
| 4 | 3 |
| 5 | 4 |
| 6 | 2 |
| 7 | 5 |
| 8 | 8 |
Find the median for the following data set:
| \text{Score} | \text{Frequency} | \text{Cumulative frequency} |
|---|---|---|
| 2 | 3 | 3 |
| 3 | 5 | 8 |
| 4 | 3 | 11 |
| 5 | 4 | 15 |
| 6 | 8 | 23 |
| 7 | 2 | 25 |
Find the mean for the following data set, correct to one decimal place:
| \text{Score } (x) | \text{Frequency } (f) | xf |
|---|---|---|
| 2 | 7 | 14 |
| 3 | 2 | 6 |
| 4 | 8 | 32 |
| 5 | 5 | 25 |
| 6 | 4 | 24 |
| 7 | 7 | 49 |
A statistician organised a set of data into the following frequency table:
Complete the frequency distribution table.
Find the mean, correct to two decimal places.
| \text{Score }(x) | \text{Frequency }(f) | xf |
|---|---|---|
| 5 | 14 | |
| 7 | 4 | |
| 9 | 2 | |
| 11 | 18 | |
| 13 | 6 | |
| \text{Total} |
Consider the data provided in the table:
Find the range.
Find the mode.
| \text{Score} | \text{Frequency} |
|---|---|
| 68 | 16 |
| 69 | 41 |
| 70 | 30 |
| 71 | 31 |
| 72 | 49 |
| 73 | 29 |
Consider the following data set:
27,\, 25,\, 24,\, 24,\, 24,\, 24,\, 24,\, 25,\, 23,\, 24,\, 26,\, 23,\, 27,\\ 23,\, 24,\, 27,\, 23,\, 23,\, 27,\, 25,\, 24,\, 24,\, 27,\, 25,\, 23
Construct a frequency distribution table for the data.
Find the mean, correct to one decimal place.
Find the range.
Find the mode.
Complete the frequency table below based on the following data set:
36,\, 50,\, 66,\, 46,\, 78,\, 63,\, 58,\, 39,\, 84,\, 40,\, 81,\, 45,\, 86,\\ 51,\, 68,\, 43,\, 64,\, 67,\, 37,\, 68,\, 48,\, 65,\, 60,\, 82,\, 75
| \text{Class} | \text{Frequency} |
|---|---|
| 30 - 39 | |
| 40 - 49 | |
| 50 - 59 | |
| 60 - 69 | |
| 70 - 79 | |
| 80 - 89 |
Complete the frequency table below based on the following data set:
25,\, 49,\, 27,\, 34,\, 28,\, 46,\, 21,\, 47,\, 36,\, 43,\, 41,\, 37,\, 37,\\ 23,\, 36,\, 37,\, 43,\, 48,\, 36,\, 40,\, 34,\, 39,\, 29,\, 46,\, 30
| \text{Class} | \text{Class centre } (x) | \text{Frequency } (f) | xf |
|---|---|---|---|
| 21 - 25 | 23 | ||
| 26 - 30 | 28 | ||
| 31 - 35 | 33 | ||
| 36 - 40 | 38 | ||
| 41 - 45 | 43 | ||
| 46 - 50 | 48 |
Complete the following frequency tables:
| \text{Class} | \text{Frequency} | \text{Cumulative frequency} |
|---|---|---|
| 10 - 19 | 3 | |
| 20 - 29 | 9 | |
| 30 - 39 | 9 | |
| 40 - 49 | 4 | |
| 50 - 59 | 2 | |
| 60 - 69 | 7 |
| \text{Class} | \text{Class centre } (x) | \text{Frequency } (f) | xf |
|---|---|---|---|
| 11 - 15 | 13 | 6 | |
| 16 - 20 | 18 | 8 | |
| 21 - 25 | 23 | 2 | |
| 26 - 30 | 28 | 2 | |
| 31 - 35 | 33 | 5 | |
| 36 - 40 | 38 | 1 |
Construct a cumulative frequency table for the following data set. Use class intervals of 40 - 49, 50 - 59, 60 - 69, etc.
77,\, 54,\, 53,\, 56,\, 73,\, 55,\, 94,\, 95,\, 76,\, 52,\, 72,\, 46,\, 85,\\ 61,\, 48,\, 90,\, 64,\, 70,\, 40,\, 52,\, 57,\, 88,\, 59,\, 95,\, 61
Consider the following frequency table:
Complete the table.
Calculate an estimate for the mean. Round your answer to two decimal places.
| \text{Class} | \text{Class} \\ \text{centre } (x) | f | xf |
|---|---|---|---|
| 1 - 9 | 8 | ||
| 10 - 18 | 6 | ||
| 19 - 27 | 4 | ||
| 28 - 36 | 6 | ||
| 37 - 45 | 8 | ||
| \text{Total} |
State the modal class of the following data set:
| \text{Class} | \text{Frequency} |
|---|---|
| 30 - 39 | 8 |
| 40 - 49 | 5 |
| 50 - 59 | 4 |
| 60 - 69 | 3 |
| 70 - 79 | 3 |
| 80 - 89 | 2 |
Estimate the median for the following data set:
| \text{Class} | \text{Frequency} | \text{Cumulative frequency} |
|---|---|---|
| 21 - 25 | 4 | 4 |
| 26 - 30 | 3 | 7 |
| 31 - 35 | 3 | 10 |
| 36 - 40 | 2 | 12 |
| 41 - 45 | 5 | 17 |
| 46 - 50 | 8 | 25 |
Estimate the mean for the following data set, correct to one decimal place:
| \text{Class} | \text{Class centre } (x) | \text{Frequency } (f) | xf |
|---|---|---|---|
| 6 - 10 | 8 | 2 | 16 |
| 11 - 15 | 13 | 1 | 13 |
| 16 - 20 | 18 | 9 | 162 |
| 21 - 25 | 23 | 8 | 184 |
| 26 - 30 | 28 | 7 | 196 |
| 31 - 35 | 33 | 5 | 165 |
Consider the frequency table:
Estimate the mean, correct to one decimal place.
State the modal group of scores.
| \text{Score} | \text{Frequency} |
|---|---|
| 1 - 5 | 20 |
| 6-10 | 15 |
| 11 - 15 | 8 |
| 16 - 20 | 4 |
| 21 - 25 | 3 |
| 26 - 30 | 2 |
Mr. Rodriguez recorded the number of pets owned by each of the students in his class. He found that 14 people had no pets, 17 people had one pet, 5 people had two pets and 9 people had three pets.
Construct a frequency table of the data.
How many students were surveyed?
The frequency table below shows the resting heart rate of some people taking part in a study:
Complete the frequency table.
Use the class centres to estimate the mean resting heart rate, to two decimal places.
| \text{Heart rate} | \text{Class}\\ \text{centre } (x) | \text{Freq.}(f) | xf |
|---|---|---|---|
| 30-39 | 13 | ||
| 40-49 | 22 | ||
| 50-59 | 24 | ||
| 60-69 | 36 |
Ben asked 35 people about how many siblings they have. He found that 12 people had no siblings, 15 people had one sibling, 3 people had two siblings and 5 people had three siblings.
Construct a frequency table of Ben's results.
In a survey the mass (in grams) of 30 individual apples from an orchard were noted and recorded in the following list:
86,\quad 87,\quad 91,\quad 93,\quad 94,\quad 95,\quad 96,\quad 96,\quad 98,\quad99
100,\quad 101,\quad 102,\quad 103,\quad 103,\quad 104,\quad 104,\quad 105,\quad 106,\quad 106
106,\quad 107,\quad 107,\quad 107,\quad 108,\quad 108,\quad 109,\quad 109,\quad 109,\quad 109
Complete the given frequency table.
Using the class centres, estimate the median.
How does this compare to the median in the individual data? Explain your answer.
| \text{Weight (g)} | \text{Class} \\ \text{centre} | \text{Frequency} |
|---|---|---|
| 85\leq x \lt 90 | 87.5 | |
| 90\leq x \lt 95 | 3 | |
| 95\leq x \lt 100 | ||
| 100\leq x \lt 105 | ||
| 105\leq x \lt 110 |