Are you wondering how to find and practice problems on the median of raw data? This is the right page for you all as it is holding with the **Worksheet on Median of Ungrouped Data**. Make use of this statistics median of discrete data worksheet pdf and solve all types of questions with flexibility. Also, you can bridge all your weak areas by answering the questions involved in the worksheet of the median of ungrouped data. Try to memorize all median formulas & tricks from our median of ungrouped data activity sheet pdf and solve the questions effortlessly.

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### Activity for Median of Ungrouped Data PDF

**Example 1:**

The weight of 5 ice bars in grams is 141, 152, 135, 117, 120. Find the median.

**Solution:**

Given data is 141, 152, 135, 117, 120

Arrange the data in ascending order: 117, 120, 135, 141, 152

The number of observations is 5, which is odd

Median = Middle Number or n+2/2

= 5+1/2

= 6/2

= 3rd observation

= 135

Hence, the median of the weight of 5 ice bars in grams is** 135.**

**Example 2:**

Find the median of the first 5 prime numbers.

**Solution:**

The first five prime numbers are 2, 3, 5, 7, 11. It is in an ordered form.

Next, find the number of observations ie., 5 which is odd.

Therefore, the middle value **5** is the median of the first five prime numbers.

**Example 3:**

Find the median of the following:

(i) The first eight even natural numbers

(ii) 8, 0, 2, 4, 3, 4, 6

**Solution:**

(i) The first eight even natural numbers are 2,4,6,8,10,12,14,16

The total number of observations = 8, which is even.

Therefore, the median is the mean of the 4th and 5th observations, ie.,

Median = Mean {4th + 5th variant}

= 1/2{8 + 10}

= 18/2

= **9**

(ii) Given data is 8, 0, 2, 4, 3, 4, 6

Sort them in ordered form (ascending order): 0, 2, 3, 4, 4, 6, 8

Total number of observations = 7, which is odd

Hence median is the middle value( 4th variant) ie., **4.**

**Example 4:
**Find the median of 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22

**Solution:**

Given data is 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22

First sort the given raw data in ascending order: 6,8,9,13,15,16,18,20,21,22,25

The total number of variants (n) = 11, which is odd.

Hence, median = value of 1/2(n+1)th observation.

= 1/2(11+1)th

= 1/2(12)th

= 6th observation

Therefore, the value of 6th observation is 16.

Hence, the median is **16.**

**Example 5:**

Find the median of the following data.

Variates: 10, 11, 12, 13, 14

Frequency: 1, 2, 3, 4, 5

**Solution:**

First, arrange the variates in ascending order, we get

10, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14

The number of variates = 15, which is odd.

Hence, Median = n+1/2th variate

= 15+1/2th

= 16/2th

= 8th variate

=** 13.**

**Example 6:**

The marks obtained by 10 students in a class test are given below.

Marks Obtained |
Number of Students |

10 7 9 5 |
4 3 2 1 |

Calculate the median of marks obtained by the students?

**Solution:**

Given 10, 10, 10, 10, 7, 7, 7, 9, 9, 5

Sorting the variates in ascending order, we get

5, 7, 7, 7, 9, 9, 10, 10, 10, 10

The number of variates = 10, which is even.

Hence, median = mean of 10/2th and (10/2+1)th variate

= mean of 5th and 6th variate

= mean of 9 and 9

= 9+9/2

= 18/2

= **9.**

**Example 7:**

Find the median of the first four odd integers. If the fifth odd integer is also included, find the difference of medians in the two cases.

**Solution:**

Take the first four odd integers in ascending order, we get

1, 3, 5, 7.

The number of variates = 4, which is even.

Hence, median = mean of 2nd and 3rd variate

= 1/2 (3+5)

= 8/2

= 4

When the fifth integer is included, we have (in ascending order)

1, 3, 5, 7, 9

Now, the number of variates = 5, which is odd.

Therefore, median = 5+1/2th

= 6/2th

= 3rd variate

= 5

Hence, the difference of medians in the two cases = 4 – 5 = -1.