Here are Paul's scores from his last 13 rounds of golf played:64, \, 66, \, 68, \, 70, \, 72, \, 74, \, 78, \, 84, \, 102, \, 106, \, 112, \, 124, \, 128
Determine his median score.
Determine the lower quartile score.
Determine the upper quartile score.
There is a test to measure the Emotional Quotient (EQ) of an individual. Here are the EQ results for 21 people listed in ascending order:90,\, 90,\, 91,\, 92,\, 93,\, 94,\, 95,\, 95,\, 95,\, 97,\, 99,\, 100,\, 108,\, 114,\, 116,\, 116,\, 117,\, 118,\, 118,\, 122,\, 129
Determine the median EQ score.
Determine the upper quartile score.
Determine the lower quartile score.
Here are Adam's scores from his last 17 exams:38, \, 44, \, 48, \, 51, \, 56, \, 58, \, 62, \, 70, \, 74, \, 78, \, 80, \, 82, \, 85, \, 88, \, 92, \, 94, \, 100
Determine his median score.
Determine the lower quartile score.
Determine the upper quartile score.
Consider the following set of scores:10,\, 11,\, 12,\, 13,\, 15,\, 17, \,19,\, 20
Within what two scores from the set do the middle 50\% of scores lie (inclusive)?
The table shows the luggage weight, in kilograms, of 30 passengers:
Find the mean check in weight, correct to two decimal places.
Determine the median, \text{Q}1, and \text{Q}3.
In which quartile does the mean lie?
| Weight | Frequency |
|---|---|
| 16 | 5 |
| 17 | 5 |
| 18 | 2 |
| 19 | 4 |
| 20 | 6 |
| 21 | 4 |
| 22 | 4 |
Consider the following data set containing 20 scores:11, \, 12, \, 18, \, 18, \, 21, \, 22, \, 22, \, 25, \, 27, \, 28, \, 29, \, 29, \, 29, \, 30, \, 32, \, 36, \, 40, \, 41, \, 45, \, 47
State the number of scores in one decile.
Find the value of the second decile.
Find the percentage of scores that fall below the seventh decile.
Find the 80th percentile.
Find the median.
Find the decile that separates the bottom 40\% of scores from the top 60\% of scores.
Consider the following data set containing 20 scores:3, \, 9, \, 11, \, 12, \, 12, \, 13, \, 15, \, 15, \, 17, \,17, \, 19, \, 22, \, 22, \, 24, \, 29, \, 32, \, 33, \, 36, \, 38, \, 38
Find the value of the sixth decile.
Find the percentage of scores that fall below 16.
Find the 10th percentile.
Find the first quartile.
Determine whether the following are the same as D_5:
The third quartile
The first quartile
The 25th percentile
The 75th percentile
The median
The 50th percentile
Consider the following data set containing 30 scores:10, \quad 11, \quad 11, \quad 13, \quad 14, \quad 15, \quad 15, \quad 16, \quad 18, \quad 24, \quad 27, \quad 28, \quad 32, \quad 33, \quad 37, \\ 42, \quad 42, \quad 44, \quad 46, \quad 49, \quad 51, \quad 53, \quad 53, \quad 55, \quad 58, \quad 60, \quad 61, \quad 64, \quad 67, \quad 67
State the number of scores in each decile.
Find the value of the 30th percentile.
Find the percentage of scores that fall above the eighth decile.
Find the second decile.
Find the median.
Find the interquartile range.
Consider the following data set containing 30 scores:6.0, \enspace 6.1, \enspace 6.1, \enspace 6.3, \enspace 6.4, \enspace 6.5, \enspace 6.5, \enspace 6.6, \enspace 6.8, \enspace 7.4, \enspace 7.7, \enspace 7.8, \enspace 8.2, \enspace 8.3, \enspace 8.7, \\ \enspace 9.2, \enspace 9.2, \enspace 9.4, \enspace 9.6, \enspace 9.9, \enspace 10.1, \enspace 10.3, \enspace 10.4, \enspace 10.5, \enspace 10.8, \enspace 11.0, \enspace 11.1, \enspace 11.4, \enspace 11.7, \enspace 11.7
Find the value of the 40th percentile.
Find the 90th percentile.
Find the decile that separates the bottom 30\% of scores from the top 70\% of scores.
Consider the following data set containing 100 scores in a 10 \times 10 grid:
| 21 | 27 | 32 | 48 | 54 | 59 | 67 | 76 | 84 | 93 |
| 21 | 27 | 33 | 49 | 54 | 59 | 68 | 77 | 84 | 93 |
| 22 | 28 | 37 | 50 | 55 | 60 | 69 | 77 | 86 | 93 |
| 23 | 29 | 39 | 50 | 56 | 61 | 69 | 79 | 86 | 94 |
| 23 | 29 | 40 | 51 | 57 | 62 | 69 | 79 | 86 | 95 |
| 24 | 30 | 40 | 52 | 57 | 62 | 71 | 81 | 87 | 96 |
| 24 | 30 | 42 | 52 | 57 | 63 | 73 | 81 | 90 | 98 |
| 25 | 31 | 43 | 52 | 57 | 63 | 75 | 82 | 91 | 98 |
| 26 | 31 | 44 | 53 | 58 | 64 | 75 | 84 | 91 | 99 |
| 26 | 31 | 47 | 53 | 58 | 67 | 76 | 84 | 91 | 99 |
Find the median.
Find the 20th percentile.
Find the third quartile.
Find the value of the 85th percentile.
Find the fourth decile.
Find the percentile with value of 57.5.
The airline Flo Air decided to keep track of flight delay times (the number of minutes after the scheduled time when the plane takes off) over a week. The 100 results are shown in the dot plot:
Determine the median delay time of the flights, in minutes.
Determine the lower quartile.
Determine the upper quartile.
Determine the interquartile range.
If a flight is delayed for 10 minutes or more, the airline incurs a fee. Based on the dot plot, how many flights did the airline incurred a fee?
What percentage of flights did the airline incur a fee?
A rival airline, Fly Air, had a mean delay time during the same week of 45 minutes. How many delayed flights did Flo Air have that were longer than 45 minutes?
What percentage of Flo Air’s flights had delay times that were longer than Fly Air’s mean delay time?
Consider the following chart showing the range of heights for boys aged 10 to 18 years:
(Credit: State Government of Victoria, Department of Education and Training)
Lachlan is 15 and his height is at the 9th decile. Select the correct range of heights for Lachlan from the following:
182 - 185\text{ cm}
177 - 181 \text{ cm}
167 - 172 \text{ cm}
158 - 161 \text{ cm}
Robert is aged 14 and is 169 \text{ cm} tall. What percentage of boys his age are taller than him?
Quentin is aged 14 and is 150 \text{ cm} tall.
What percentage of boys his age are taller than him?
If Quentin's height continues to follow this growth chart, how tall will he be when he is 18?
Consider the following chart showing the range of heights for girls aged 10 to 18 years:
(Credit: State Government of Victoria, Department of Education and Training)
Pauline is 16 and her height is at the 5th decile. Select the correct range of heights for Pauline from the following:
160 - 165 \text{ cm}
169 - 172 \text{ cm}
152 - 155 \text{ cm}
142 - 145 \text{ cm}
Roxanne is aged 17 and is 175 \text{ cm} tall.
What percentage of girls her age are taller than her?
If Roxanne's height continues to follow this growth chart, how tall will she be when she is 18?
The following information is based on population data for the heights, in centimetres, of females aged 8 to 16:
| \text{Age} | P_3 | P_5 | P_{10} | P_{25} | P_{50} | P_{75} | P_{90} | P_{95} | P_{97} |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 117.3 | 118.5 | 120.5 | 123.9 | 127.8 | 131.9 | 135.6 | 137.9 | 139.4 |
| 9 | 121.9 | 123.2 | 125.3 | 129.0 | 133.1 | 137.4 | 141.4 | 143.8 | 145.4 |
| 10 | 126.0 | 127.5 | 129.8 | 133.7 | 138.2 | 142.8 | 147.0 | 149.6 | 151.3 |
| 11 | 130.7 | 132.4 | 135.0 | 139.4 | 144.3 | 149.2 | 153.7 | 156.4 | 158.1 |
| 12 | 137.4 | 139.2 | 142.0 | 146.5 | 151.5 | 156.4 | 160.8 | 163.5 | 165.2 |
| 13 | 144.2 | 145.9 | 148.4 | 152.7 | 157.3 | 162.0 | 166.1 | 168.6 | 170.2 |
| 14 | 148.1 | 149.7 | 152.1 | 156.0 | 160.5 | 164.9 | 168.9 | 171.3 | 172.9 |
| 15 | 149.7 | 151.3 | 153.6 | 157.5 | 161.9 | 166.3 | 170.2 | 172.6 | 174.2 |
| 16 | 150.4 | 151.9 | 154.3 | 158.2 | 162.6 | 166.9 | 170.9 | 173.2 | 174.8 |
If Rochelle is 8 years old and her height is at the tenth percentile, how tall is she?
If Caitlin is 12 years old and her height is at the third quartile, how tall is she?
Find the percentile of 13-year old females with the following heights:
148.4 \text{ cm}
162.0 \text{ cm}
Find the percentage of 13-year old females that are between 148.4 \text{ cm} and 162.0 \text{ cm}.
The following information is based on population data for the lengths of 24-month old infant boys:
The median is 87.7 \text{ cm}.
The 5th percentile is 81.8 \text{ cm}.
The 75th percentile is 90 \text{ cm}.
The 9th decile is 92.2 \text{ cm}.
The 97th percentile is 94.3 \text{ cm}.
A particular 24-month old infant boy is 82 \text{ cm} in length. Is this long for his age and gender? Explain your answer.
Exactly 10\% of infant boys are longer than William's length. Find William's length in centimetres.
Find the length in centimetres that separates the longest 25\% of infant boys from the rest of the boys.
The following information is based on population data for the head circumference of 3.5-month old infant girls:
The median is 40.5 \text{ cm}.
The 5th percentile is 38.4 \text{ cm}.
The first quartile is 39.6 \text{ cm}.
The first decile is 38.8 \text{ cm}.
The 97th percentile is 43.2 \text{ cm}.
Is a head circumference of 43 \text{ cm} considered large for a 3.5-month old infant girl? Explain your answer.
Find the percentage of 3.5-month old girl infants that have head circumferences between 38.8 \text{ cm} and 39.6 \text{ cm}.
75\% of 3.5-month old infant girls have a head circumference larger than exactly what value?
The following information is based on population data for the heights of fifteen year old males:
The third percentile is 154.6 \text{ cm}.
The 25th percentile is 164.8 \text{ cm}.
The fifth decile is 170.1 \text{ cm}.
The 95th percentile is 182.4 \text{ cm}.
If Xavier is 170 \text{ cm} tall, approximately what percentage of boys in this age group would be taller?
Approximately what percentage of fifteen year old males are between 154.6 \text{ cm} and 170.1 \text{ cm}?
If 40 fifteen year old males are randomly selected, how many would you expect to be taller than 182.4 \text{ cm}?
The following shows students and their tertiary entrance rank given as percentiles:
Derek: 78th percentile
William: 82nd percentile
Eileen: 98th percentile
Rosey: 89th percentile
Approximately what percentage of students scored equal to or above Derek?
Approximately what percentage of students scored between William and Rosey?
If there were 43\,500 students who obtained a ranking, approximately how many performed the same or above Eileen?
To gain a place in the main race of a car rally, teams must compete in a qualifying round. The median time in the qualifying round determines the cut off time to make it through to the main race. Below are some results from the qualifying round:
75\% of teams finished in 159 minutes or less.
25\% of teams finished in 132 minutes or less.
25\% of teams finished between with a time between 132 and 142 minutes.
Determine the cut off time required in the first round to make it through to the main race.
Determine the interquartile range in the qualifying round.
In the qualifying round, the ground was wet, while in the main race, the ground was dry. To make the times more comparable, the finishing time of each team from the qualifying round is reduced by 5 minutes. Find the new median time from the qualifying round.
The formula p = \dfrac{100 \left(n - r\right)}{n} can be used to calculate the percentile in which a team lies, where p is the percentile, n is the number of teams and r is the rank of the team.
Find the percentile for each of the following player's teams, rounded to the nearest whole number.
Charlie is in a table tennis league. He is ranked third out of 30 people.
Mario is in a fantasy football league. His team is ranked fifth out of 55 teams.
Roald is in a volleyball competition. His team is ranked forty-sixth out of 180 teams.
Kerry is in a basketball tournament. Her team is ranked forty-sixth out of 155 teams.