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Lesson: The Median of a Data Set

In this lesson, we will learn how to find and interpret the median of a data set.

Sample Question Videos

01:14
02:44

Worksheet • 21 Questions • 2 Videos

Q1:

The given table shows the temperatures, in Fahrenheit, of some cities in January. Find the median of the three cities with the highest temperatures.

39 27 24 23 36
43 30 39 26 16
21 41 5 22 12

Q2:

The table shows the players on a soccer team who scored goals during a season. Suppose a player that scored 15 goals was added to the table. What would the median number of goals scored be?

Player Nabil Sherif Maged Adam Fares Ramy
Goals 15 13 11 5 14 11

Q3:

Calculate the median of the values in the table.

13 13 23 20 21 13 23 13 15 22 15 19 20 18 15

Q4:

The table records the heights, in inches, of a group of fifth graders and a group of sixth graders. What is the difference between the medians of the heights of both groups?

Fifth Grade 6 5 , 6 1 , 5 9 , 5 0 , 6 1 , 6 5 , 5 4
Sixth Grade 6 0 , 5 8 , 6 5 , 6 4 , 5 3 , 5 5 , 6 4

Q5:

The table shows the marks that four students received in their end of year exams. Calculate the median mark achieved by student (D).

Students Mathematics Chemistry Physics Biology History
(A) 13 12 14 11 7
(B) 14 11 15 8 12
(C) 6 7 14 13 8
(D) 11 9 12 10 14

Q6:

The table shows the savings of a group of 8 children. Determine the median of the data.

Child Child 1 Child 2 Child 3 Child 4 Child 5 Child 6 Child 7 Child 8
Savings in Dollars 44.00 36.50 36.50 33.00 18.70 17.60 14.40 41.00

Q7:

What is the median of the following numbers: 11, 11, 8, 8, 9, 9?

Q8:

Each time she writes a script for a movie, Yasmine creates a number of drafts. For the last five movies, she wrote 7, 8, 10, 6, and 6 drafts. Find the median of the number of drafts she writes.

Q9:

For his science lab, Adam recorded the following lengths of 7 tree leaves: 2 centimetres, 7 centimetres, 7 centimetres, 5 centimetres, 6 centimetres, 3 centimetres, and 2 centimetres.

What is the median length?

Q10:

The table shows the distribution of marks students attained in a mathematics exam. By drawing a cumulative frequency curve, estimate the median mark attained.

Mark 5–9 10–14 15–19 20–24 25–29 30– Total
Frequency 5 10 9 10 12 4 50

Q11:

Find the median of the numbers in the table.

4.1 9.1 10.6 8.3 3.6 12.9 2.9 1.1 6.6 9.6 3.4

Q12:

What is the median of the following numbers: 10, 10, 7, 7, 8?

Q13:

By drawing a cumulative frequency curve, find the median of the following frequency distribution.

Sets 300–399 400–499 500–599 600–699 700– Total
Frequency 9 11 6 10 14 50

Q14:

The table shows the distribution of daily wages of 100 workers at a factory. By drawing a cumulative frequency curve, estimate the median daily wage.

Daily Wages ( LE) 15– 20– 25– 30– 35– 40– Total Number of Workers
Number of Workers 23 14 12 15 19 17 100
  • A30 LE
  • B49 LE
  • C35 LE
  • D64 LE

Q15:

The table shows the yardage gained by a team each play for five plays. By arranging the yardage in ascending order, find the median.

Play 1 2 3 4 5
Yardage 7 − 6 − 1 8 20 9

Q16:

What is the correct definition of the median of a data set?

  • A The median is the central data value. Half of the values in the data set are above the median and half are below the median.
  • B The median is the difference between the lower quartile and the upper quartile.
  • C The median is the most common data value.
  • D The median is the difference between the maximum and minimum data values.
  • E The median is the mathematical “average.” If all data values were the same, they would be equal to the median.

Q17:

The table shows the number of sold cupcakes last week. What is the median of the numbers?

Day Friday Saturday Sunday Monday Tuesday Wednesday Thursday
Number Of Sold Cupcakes 18 20 25 14 16 15 25

Q18:

The bar graph shows the percentage of different metals that make up an alloy. Is the median of the percentages 1 0 % ?

  • Ayes
  • Bno

Q19:

Find the median for the set of data in this table.

Amount Tally Frequency
15 7
35 8
50 1
75 4
90 5

Q20:

The table shows the number of hours that two students spent studying on each day of a week. Find the median number of hours spent studying by student (A).

Student (A) 9 8 5 8 4 4 6
Student (B) 4 9 3 7 6 4 9

Q21:

Data Set 1 25 22 28 51 26 28 29 32
Data Set 2 21 27 19 26 24 23 28 25

Calculate the median of each data set.

  • Adata set 1: 28, data set 2: 24.5
  • Bdata set 1: 24.5, data set 2: 28
  • Cdata set 1: 27.5, data set 2: 24.5
  • Ddata set 1:27.5, data set 2:24
  • Edata set 1:28, dataset 2:24

What do the medians reveal about the two data sets?

  • AThe central value of data set 1 is larger than that of data set 2.
  • BThe distributions of the two data sets are very similar.
  • CThe spread of the middle 50% of the values is similar for both data sets.
  • DThe central value of data set 2 is larger than the central value of data set 1.
  • EThe difference between the minimum and maximum values is similar for both data sets.
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