Worksheet: The Median of a Data Set

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

Q1:

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

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

Q2:

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

Q3:

Calculate the median of the values 2.9,5.4,5.1,3.7,3.4,1.9,6.1,8.1,12.4,2.6,8.85.5,and.

Q4:

Find the median of the values 20150320130200,,,,and.

  • A150
  • B175
  • C200
  • D164

Q5:

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

Q6:

Find the median of the values 200300330370,,,and.

Q7:

Find the median of the values 2.41.96.39.99.4,,,,and.

Q8:

Find the median of the values 10.26.212.45.6,,,and.

Q9:

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

Q10:

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 William Ethan Benjamin Daniel James Matthew
Goals 15 13 11 5 14 11

Q11:

Calculate the median of the values in the table.

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

Q12:

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

Q13:

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

Q14:

Each time she writes a script for a movie, Natalie 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.

Q15:

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

What is the median length?

Q16:

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

Q17:

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 โˆ’ 6 โˆ’ 1 8 20 9

Q18:

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

  • AThe median is the difference between the lower quartile and the upper quartile.
  • BThe median is the most common data value.
  • CThe median is the mathematical โ€œaverage.โ€ If all data values were the same, they would be equal to the median.
  • DThe median is the difference between the maximum and minimum data values.
  • EThe median is the central data value. Half of the values in the data set are above the median and half are below the median.

Q19:

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

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

What do the medians reveal about the two data sets?

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

Q22:

The table shows the hours trained per month of two athletes. Find the median number of hours trained for athlete (B).

Athlete (A) 57 63 66 54 72 60 67 61 60 74 61 52
Athlete (B) 56 74 70 63 67 46 47 68 68 52 64 51

Q23:

If you arrange a set of numbers from least to greatest, the middle number will be the median. Find the median of the numbers on these cards.

  • A 3 8 5 2 4
  • B 3 8 9 2 5
  • C 3 8 5 2 3
  • D38.6
  • E38.9

Q24:

Let ๐พ be a positive number. Given that the median of the values ๐พ+12๐พ+8๐พ+14๐พ+4๐พ+20,,,,and is 28, determine the value of ๐พ.

Q25:

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

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