Worksheet: Quartiles of a Data Set

In this worksheet, we will practice finding the median and upper and lower quartiles of a data set.

Q1:

Determine the median and quartiles of the following set of data: 56, 55, 90, 50, 41, 84, 68, 75, 92, 50, and 71.

  • A The median is 69.5, and the quartiles are 50 and 84.
  • B The median is 68, and the quartiles are 52.5 and 79.5.
  • C The median is 71, and the quartiles are 55 and 90.
  • D The median is 68, and the quartiles are 50 and 84.

Q2:

Determine the median and quartiles of the following set of data: 1.8, 1.6, 1.1, 2.4, 0.6, 1.3, 2.9, 1.5, 0.4, 1.9, 2.9.

  • A The median is 1.6, and the quartiles are 1.3 and 2.9.
  • B The median is 1.6, and the quartiles are 0.6 and 1.9.
  • C The median is 1.8, and the quartiles are 1.1 and 2.4.
  • D The median is 1.6, and the quartiles are 1.1 and 2.4.

Q3:

Determine the upper and the lower quartiles of the following set of data: 114, 103, 50, 52, 95, 103, 93, 53, 65, 57, 52, 89, 111, 89, and 96.

  • Alower quartile = 5 3 , upper quartile = 8 9
  • Blower quartile = 5 0 , upper quartile = 8 9
  • Clower quartile = 8 9 , upper quartile = 1 0 3
  • Dlower quartile = 5 3 , upper quartile = 1 0 3
  • Elower quartile = 5 0 , upper quartile = 1 0 3

Q4:

A set of data’s minimum is 3.44, its lower quartile is 7.42, its median is 7.74, its upper quartile is 14.02, and its maximum is 17.74. Between which two values does the middle 5 0 % of the data lie?

  • A7.74 and 17.74
  • B3.44 and 7.74
  • C7.42 and 7.74
  • D7.42 and 14.02
  • E7.74 and 14.02

Q5:

The table shows the capacities of 6 sports stadiums around the world. Describe how the lower quartile will be affected if @Emiratesstem, London, United Kingdom, which has a capacity of 60‎ ‎338, is included in the data.

Stadium Location Capacity
Gelora Sriwijaya Stadium Palembang, Indonesia 40‎ ‎000
Olympiastadion Berlin, Germany 74‎ ‎228
Frankenstadion Nuremberg, Germany 48‎ ‎548
Memorial Stadium Nebraska, United States 86‎ ‎047
Borg El Arab Stadium Alexandria, Egypt 86‎ ‎000
Stamford Bridge London, United Kingdom 42‎ ‎055
  • AThe lower quartile will remain unchanged at 42‎ ‎058.
  • BThe lower quartile will increase from 42‎ ‎055 to 42‎ ‎058.
  • CThe lower quartile will decrease from 42‎ ‎058 to 42‎ ‎055.
  • DThe lower quartile will remain unchanged at 42‎ ‎055.
  • EThe lower quartile will increase from 42‎ ‎055 to 86‎ ‎047.

Q6:

Determine the median and quartiles of the following set of data: 1,350, 1,400, 1,250, 1,050, 1,450, 1,150, 1,000.

  • A The median is 1,250, and the quartiles are 1,100 and 1,375.
  • B The median is 1,250, and the quartiles are 1,150 and 1,350.
  • C The median is 1,350, and the quartiles are 1,050 and 1,400.
  • D The median is 1,250, and the quartiles are 1,050 and 1,400.

Q7:

Determine the upper and the lower quartiles of the following set of data: 19.4, 42.1, 56.1, 27.5, 5.3, 49.9, 48.8, 44.3, 13.1, 15.4, 20.1, 4.1, 38.1, 33.8, and 41.5.

  • Alower quartile = 15.4, upper quartile = 33.8
  • Blower quartile = 4.1, upper quartile = 33.8
  • Clower quartile = 33.8, upper quartile = 44.3
  • Dlower quartile = 15.4, upper quartile = 44.3
  • Elower quartile = 4.1, upper quartile = 44.3

Q8:

Karim’s history test scores are 74, 96, 85, 90, 71, and 98. Determine the upper and lower quartiles of his scores.

  • Alower quartile = 74, upper quartile = 87.5
  • Blower quartile = 96, upper quartile = 74
  • Clower quartile = 87.5, upper quartile = 96
  • Dlower quartile = 74, upper quartile = 96
  • Elower quartile = 71, upper quartile = 98

Q9:

Sameh’s scores in a card game were 4, 2 , 1 , 5 , 5 , 7, and 0. Determine the lower quartile and upper quartile of his scores.

  • Alower quartile = 2 , upper quartile = 4
  • Blower quartile = 4, upper quartile = 5
  • Clower quartile = 5 , upper quartile = 1
  • Dlower quartile = 5 , upper quartile = 4
  • Elower quartile = 1 , upper quartile = 4

Q10:

Select the pair of data sets which have the same median and quartiles, but different ranges.

  • A30, 41, 34, 34, 35, 49 and 31, 35, 42, 50, 35, 36
  • B16, 15, 25, 20, 16, 28 and 17, 15, 15, 28, 27, 20
  • C58, 68, 57, 58, 54, 69 and 58, 69, 58, 54, 59, 57
  • D10, 10, 9, 11, 7, 8 and 6, 8, 10, 21, 9, 10
  • E83, 77, 73, 88, 71, 84 and 69, 68, 58, 57, 62, 73

Q11:

The table shows the savings of a group of 8 children. Determine the lower and upper quartiles of the data.

Child Child 1 Child 2 Child 3 Child 4 Child 5 Child 6 Child 7 Child 8
Savings in Dollars 35.00 30.40 18.30 23.40 29.50 21.50 33.50 18.40
  • ALower quartile = $19.95, upper quartile = $26.45
  • BLower quartile = $31.95, upper quartile = $19.95
  • CLower quartile = $26.45, upper quartile = $31.95
  • DLower quartile = $19.95, upper quartile = $31.95
  • ELower quartile = $18.30, upper quartile = $35.00

Q12:

The table shows the number of students who partake in different physical activities. Find the lower and upper quartiles of the data.

Activity Basketball Cycling Soccer Running Rope Jumping Swimming Climbing
Number of Students 7 12 6 14 15 6 11
  • Alower quartile: 6, upper quartile: 11
  • Blower quartile: 4, upper quartile: 12
  • Clower quartile: 11, upper quartile: 14
  • Dlower quartile: 6, upper quartile: 14
  • Elower quartile: 6, upper quartile: 15

Q13:

The table shows DVD prices in dollars at various shops. What are the lower and upper quartiles of the data?

19.86 23.82 17.27 24.01
23.56 18.74 16.79 15.57
23.39 20.86 23.04 20.25
  • Alower quartile = 18.74, upper quartile = 20.25
  • Blower quartile = 23.475, upper quartile = 18.005
  • Clower quartile = 18.005, upper quartile = 20.555
  • Dlower quartile = 18.005, upper quartile = 23.475
  • Elower quartile = 20.555, upper quartile = 23.475

Q14:

The number of goals scored by 12 football players during a season is 10, 9, 14, 20, 19, 20, 9, 5, 12, 9, 19, and 7. State whether the following statement is true or false: About three-fourths of the players scored 19 or more.

  • Afalse
  • Btrue

Q15:

The line plot shows the magnitudes of several recent earthquakes. Determine the upper and lower quartiles.

  • Alower quartile = 2 . 3 , upper quartile = 2 . 7
  • Blower quartile = 3 . 3 , upper quartile = 2 . 3
  • Clower quartile = 2 . 7 , upper quartile = 3 . 3
  • Dlower quartile = 2 . 3 , upper quartile = 3 . 3
  • Elower quartile = 2 , upper quartile = 3 . 5

Q16:

If 𝑄 𝑄 𝑄 𝑄 3 2 2 1 , what does this suggest about the shape of the distribution?

  • AIt is positively skewed.
  • BIt is negatively skewed.
  • CIt is symmetrical.

Q17:

The times taken for a bus journey between two towns are normally distributed with mean 28 minutes and standard deviation 4 minutes. Calculate the lower and upper quartiles of the times taken. Round your answer to the nearest integer.

  • Alower quartile = 20, upper quartile = 36
  • Blower quartile = 22, upper quartile = 34
  • Clower quartile = 27, upper quartile = 29
  • Dlower quartile = 25, upper quartile = 31
  • Elower quartile = 26, upper quartile = 32

Q18:

If 𝑄 𝑄 > 𝑄 𝑄 , what type of skewness does this indicate?

  • Apositive skew
  • Bnegative skew

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