What is Median?

The median is the middle number in a set of numbers arranged in order.
If there are two middle numbers, the median is their average.

Where is Median Used?

• In math to find the center value of a data set.

• In finance to report median income or house prices (more accurate than average in some cases).

• In science to analyze experimental results.

• In sports to see the middle performance score.

• In education to compare test results fairly (avoiding extreme highs/lows).

How to Calculate the Median – Step-by-Step

Step 1: Arrange the numbers from smallest to largest.

Step 2: Count how many numbers are in the list.

Step 3:

• If the number of values is odd, the middle number is the median.

• If the number of values is even, add the two middle numbers and divide by 2.

What is an Outlier?

An outlier is a number in a data set that is very different (much higher or lower) than the rest of the numbers.

Does an Outlier Affect the Median?

No
The median is the middle number, so outliers do not change it , the middle stays the same.

Choosing Between Mean, Median, and Mode

Questions

Criterion A: Knowledge and Understanding – Median

1. Basic Median

Find the median of: 4, 8, 6, 3, 5

2. Median of Test Scores

A student’s scores are: 78, 85, 92, 88, 90
What is the median score?

3. Median of Even Set

Find the median of: 10, 15, 12, 8, 20, 18

4. Ordered List

Find the median of: 22, 19, 25, 17, 21, 23, 20

5. Missing Number from a Median

Five numbers have a median of 18. Four of the numbers are: 12, 15, 22, and 25.
What is the missing number?

6. Median of Repeated Numbers

Find the median: 5, 7, 7, 8, 9, 9, 10

7. Median of Daily Steps

Steps recorded over five days: 4,200, 4,600, 4,800, 5,000, 4,700
What is the median?

Criterion D: Real-Life Problems on Median

1. Median of Test Results

A student scored the following marks in six weekly tests: 75, 82, 89, 78, 80, 85

a) What is the median score?
b) Why might the median be more useful than the average here?
c) If one very low score is added, does the median change a lot?

2. Travel Time to School

A student recorded their travel times in minutes: 12, 15, 13, 17, 14

a) Find the median travel time.
b) Is this a good way to estimate how long it takes to get to school?
c) Would you rather use mean or median to plan your schedule? Why?

3. Ice Cream Sales

Number of ice creams sold per day: 120, 130, 125, 140, 150, 300, 135

a) Find the median.
b) Does the 300 sale day affect the median much?
c) Is the median or mean better for showing a typical sales day?

4. Median Heights of Students

Heights (in cm): 150, 152, 155, 160, 162, 170, 175

a) Find the median height.
b) Why might a PE teacher care about the median height?
c) If a very tall student joins (height = 190 cm), how does it affect the median?

5. Median of Pocket Money

Weekly pocket money of students ($): 5, 6, 10, 4, 8, 7, 20

a) What is the median amount?
b) Is the median a better measure than the mean in this case? Why?
c) If you remove the $20, how does the median change?

6. Median Daily Screen Time

Screen time (in minutes): 90, 100, 120, 130, 200

a) Find the median screen time.
b) What does this say about the student’s daily usage?
c) How could this help parents set screen time rules?

7. Median for Planning Events

A teacher asked how many classmates students would invite to a party. Results: 5, 6, 10, 5, 7, 5, 8

a) Find the median.
b) How might the teacher use this info to prepare enough food?
c) Would it be helpful to also know the range? Why?

  Answers

(Criterion A)

1. Ordered: 3, 4, 5, 6, 8 → Median = 5

2. Ordered: 78, 85, 88, 90, 92 → Median = 88

3. Ordered: 8, 10, 12, 15, 18, 20 → (12 + 15) ÷ 2 = 13.5

4. Ordered: 17, 19, 20, 21, 22, 23, 25 → Median = 21

5. 12, 15, ?, 22, 25

   To keep the median at 18, the number in the middle (3rd) position must be 18.

   Missing number = 18

6. Ordered list already → Median = 8

7. Ordered: 4,200; 4,600; 4,700; 4,800; 5,000 → Median = 4,700

Answers (Criterion D)

1. a) Ordered: 75, 78, 80, 82, 85, 89 → (80+82)/2 = 81
   b) Median isn’t affected by outliers.
   c) No, median stays stable with one low score.

2. a) Ordered: 12, 13, 14, 15, 17 → Median = 14
   b) Yes, it shows the middle of all trips.
   c) Median, because it ignores extreme days.

3. a) Ordered: 120, 125, 130, 135, 140, 150, 300 → Median = 135
   b) No, 300 doesn’t affect the middle.
   c) Median is better because the 300 is an outlier.

4. a) Ordered list → Median = 160 cm
   b) Helps estimate average equipment sizes.
   c) Median remains the same — less affected by outliers.

5. a) Ordered: 4, 5, 6, 7, 8, 10, 20 → Median = 7
   b) Yes, mean would be higher because of $20.
   c) Median stays the same: 7

6. a) Ordered: 90, 100, 120, 130, 200 → Median = 120
   b) Student uses about 2 hours a day.
   c) Helps manage healthy limits.

7. a) Ordered: 5, 5, 5, 6, 7, 8, 10 → Median = 6
   b) Helps predict average number of guests.
   c) Yes, range helps show how much the numbers vary.