The median of the following data will be _________. 32, 25, 33, 27, 35, 29 and 30
30
Finding the Median of a Data Set
The question asks us to find the median of the given data set: 32, 25, 33, 27, 35, 29, and 30.
Understanding the Median
The median is a measure of central tendency. It is the middle value in a data set that is ordered from least to greatest. To find the median, we need to follow these steps:
- Arrange the data set in ascending (or descending) order.
- Count the number of observations (n) in the data set.
- If n is an odd number, the median is the middle observation, located at the $\left(\frac{n+1}{2}\right)^\text{th}$ position.
- If n is an even number, the median is the average of the two middle observations, located at the $\left(\frac{n}{2}\right)^\text{th}$ and $\left(\frac{n}{2}+1\right)^\text{th}$ positions.
Step-by-Step Calculation of the Median
Let's apply these steps to the given data set: 32, 25, 33, 27, 35, 29, 30.
Step 1: Arrange the data in ascending order
The given data set in ascending order is:
- 25
- 27
- 29
- 30
- 32
- 33
- 35
The ordered data set is: 25, 27, 29, 30, 32, 33, 35.
Step 2: Count the number of observations (n)
Let's count the numbers in the data set: 32, 25, 33, 27, 35, 29, 30. There are 7 numbers.
So, n = 7.
Step 3: Determine the median based on n
Since n = 7 is an odd number, the median is the value at the $\left(\frac{n+1}{2}\right)^\text{th}$ position.
Position of the median $= \left(\frac{7+1}{2}\right)^\text{th} = \left(\frac{8}{2}\right)^\text{th} = 4^\text{th}$ position.
Step 4: Identify the value at the median position
Looking at the ordered data set (25, 27, 29, 30, 32, 33, 35), the value at the 4th position is 30.
Therefore, the median of the given data set is 30.
Summary of Median Calculation
| Step | Description | Result |
|---|---|---|
| 1 | Original Data | 32, 25, 33, 27, 35, 29, 30 |
| 2 | Sorted Data (Ascending) | 25, 27, 29, 30, 32, 33, 35 |
| 3 | Number of observations (n) | 7 |
| 4 | Position of Median ($\frac{n+1}{2}$) | $\frac{7+1}{2} = 4^\text{th}$ position |
| 5 | Value at Median Position | 30 |
Revision Table: Measures of Central Tendency
| Measure | Description | How to Calculate |
|---|---|---|
| Mean | The average of all values. | Sum of all values / Number of values |
| Median | The middle value when data is ordered. | Sort data, find middle term (or average of two middle terms). |
| Mode | The value that appears most frequently. | Identify the value with the highest frequency. |
Additional Information on Median and Data
The median is particularly useful when a data set contains outliers, as it is not affected by extremely large or small values in the same way the mean is. It represents the exact middle point of the data distribution.
For an even number of data points, say n=8, the median would be the average of the values at the $\frac{8}{2}=4^\text{th}$ and $\frac{8}{2}+1=5^\text{th}$ positions in the sorted list.
Similar Questions
The given table represents the monthly income of 100 families of a locality.
Monthly income range (in Rs.)
Number of families
Income more than Rs. 10,000
100
Income more than Rs. 13,000
85
Income more than Rs. 16,000
69
Income more than Rs. 19,000
50
Income more than Rs. 22,000
33
Income more than Rs. 25,000
15
The number of families having income range (in Rs.) 19000 - 22000 is:
Find the mode for the given distribution (rounded off to two decimal places).
Class Interval 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 8 7 6 9 11 10 The arithmetic mean of the following data is _________.
23, 17, 20, 19, 21
For a sample data, mean = 60 and median = 48. For this distribution, the mode is:
The mode of the following data is __________.
13, 15, 31, 12, 27, 13, 27, 30, 27, 28 and 16
The median of a set of 11 distinct observations is 73.2. If each of the largest five observations of the set is increased by 3, then the median of the new set:
What is the mode of the given data?
5, 7, 9, 7, 3, 7, 5, 7, 8, 6, 7
In tossing a coin, let the probability of turning up a head be p . The hypotheses are H 0∶ p = 0.4 vs H 1 ∶ p = 0.6. H 0is rejected if there are five or more heads in six tosses. Then the power of the test is:
For ANOVA two-way classification, to test two types of cloth in fashion trends, we have the following table.
Source of Variations
SS
Df
MSS
F-Ratio
Variety A
280
2
140
42.04
Variety B
α
3
34.03
Error
20
β
3.33
Total
640
11
The values of (α, β) are:The arithematic average of Edgeworth - Marshal index number
Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2What is the mode of the given data?
21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
