Solved Questions on Mean, Median, and Mode
Question 1: Study the bar graph given below and find the mean, median, and mode of the given data set.
Solution:
Mean = (sum of all data values) / (number of values)
Mean = (5 + 7 + 9 + 6) / 4
= 27 / 2
= 6.75Order the given data in ascending order as: 5, 6, 7, 9
Here, n = 4 (which is even)
Median = [(n/2)th term + {(n/2) + 1}th term] / 2
Median = (6 + 7) / 2
= 6.5Mode = Most frequent value
= 9 (highest value)Range = Highest value – Lowest value
Range = 9 – 5
= 4
Question 2: Find the mean, median, mode, and range for the given data
190, 153, 168, 179, 194, 153, 165, 187, 190, 170, 165, 189, 185, 153, 147, 161, 127, 180
Solution:
For Mean:
190, 153, 168, 179, 194, 153, 165, 187, 190, 170, 165, 189, 185, 153, 147, 161, 127, 180
Number of observations = 18
Mean = (Sum of observations) / (Number of observations)
= (190+153+168+179+194+153+165+187+190+170+165+189+185+153+147 +161+127+180) / 18
= 2871/18
= 159.5
Therefore, the mean is 159.5
For Median:
The ascending order of given observations is,
127, 147, 153, 153, 153, 161, 165, 165, 168, 170, 179, 180, 185, 187, 189, 190, 190, 194
Here, n = 18
Median = 1/2 [(n/2) + (n/2 + 1)]th observation
= 1/2 [9 + 10]th observation
= 1/2 (168 + 170)
= 338/2
= 169Thus, the median is 169
For Mode:
The number with the highest frequency = 153
Thus, mode = 53
For Range:
Range = Highest value – Lowest value
= 194 – 127
= 67
Question 3: Find the Median of the data 25, 12, 5, 24, 15, 22, 23, 25
Solution:
25, 12, 5, 24, 15, 22, 23, 25
Step 1: Order the given data in ascending order as:
5, 12, 15, 22, 23, 24, 25, 25
Step 2: Check n (number of terms of data set) is even or odd and find the median of the data with respective ‘n’ value.
Step 3: Here, n = 8 (even) then,
Median = [(n/2)th term + {(n/2) + 1)th term] / 2
Median = [(8/2)th term + {(8/2) + 1}th term] / 2
= (22+23) / 2
= 22.5
Question 4: Find the mode of given data 15, 42, 65, 65, 95.
Solution:
Given data set 15, 42, 65, 65, 95
The number with highest frequency = 65
Mode = 65
Mean, Median and Mode
Mean, Median, and Mode are measures of the central tendency. These values are used to define the various parameters of the given data set. The measure of central tendency (Mean, Median, and Mode) gives useful insights about the data studied, these are used to study any type of data such as the average salary of employees in an organization, the median age of any class, the number of people who plays cricket in a sports club, etc.
Let’s learn more about the Mean, Median, and Mode Formulas, Examples, and FAQs in this article.
Table of Content
- Measures of Central Tendency
- What are Mean, Median, and Mode?
- What is Mean?
- What is Median?
- What is Mode?
- Symbol of Mode
- Relation between Mean Median Mode
- What is Range?
- Differences between Mean, Median and Mode