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Worksheet: The Median of a Data Set
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 | William | Ethan | Benjamin | Daniel | James | Matthew |
|---|---|---|---|---|---|---|
| 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 | |
| Sixth Grade |
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 |
Q8:
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.
Q9:
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?
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.
| Classes | 300–399 | 400–499 | 500–599 | 600–699 | 700– | Total |
|---|---|---|---|---|---|---|
| Frequency | 9 | 11 | 6 | 10 | 14 | 50 |
- A500
- B400
- C550
- D580
- E800
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 |
- A64 LE
- B49 LE
- C35 LE
- D30 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 | 20 | 9 |
Q16:
What is the correct definition of the median of a data set?
- A The median is the mathematical “average.” If all data values were the same, they would be equal to the median.
- B The median is the most common data value.
- C The median is the difference between the maximum and minimum data values.
- D 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.
- E The median is the difference between the lower quartile and the upper quartile.
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 ?
- Ano
- Byes
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: 27.5, data set 2: 24.5
- Cdata set 1:27.5, data set 2:24
- Ddata set 1: 28, data set 2: 24.5
- Edata set 1: 24.5, data set 2: 28
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 central value of data set 2 is larger than the central value of data set 1.
- CThe difference between the minimum and maximum values is similar for both data sets.
- DThe spread of the middle 50% of the values is similar for both data sets.
- EThe distributions of the two data sets are very similar.