What is the mode of the given data? 5, 7, 9, 7, 3, 7, 5, 7, 8, 6, 7
7
Finding the Mode of a Data Set
The question asks us to find the mode of the given data set. The mode is a measure of central tendency that represents the value that appears most frequently in a data set.
The given data set is:
5, 7, 9, 7, 3, 7, 5, 7, 8, 6, 7
To find the mode, we need to count how many times each number appears in the data set. Let's list the unique numbers and their frequencies:
| Number | Frequency (Count) |
|---|---|
| 3 | 1 |
| 5 | 2 |
| 6 | 1 |
| 7 | 5 |
| 8 | 1 |
| 9 | 1 |
Looking at the frequency table, we can see that the number 7 appears 5 times, which is more than any other number in the data set.
Therefore, the number that occurs with the highest frequency is 7.
The mode of the given data set is 7.
Revision Table: Measures of Central Tendency
| Measure | Definition | How to Calculate | Use Case |
|---|---|---|---|
| Mean | The average of the data set. | Sum of all values divided by the number of values. | Good for symmetrical data without outliers. |
| Median | The middle value when the data set is ordered. | Order data, find the middle value (or average of two middle values if count is even). | Good for skewed data or data with outliers. |
| Mode | The value that appears most frequently. | Count the frequency of each value and find the one with the highest count. | Useful for categorical or discrete data; shows the most common value. |
Additional Information on Mode and Data Types
The mode is particularly useful for certain types of data:
- Categorical Data: For data that fits into categories (like favorite color, type of car), the mode is the only measure of central tendency that makes sense. You can't calculate a mean or median for non-numeric categories.
- Discrete Data: For data that can only take specific, separate values (like the number of siblings, the score on a die roll), the mode identifies the most common outcome.
- Identifying Peaks: In a frequency distribution, the mode corresponds to the peak(s) of the distribution. A data set can have one mode (unimodal), two modes (bimodal), or more (multimodal). If all values appear with the same frequency, the data set has no mode.
Understanding the mode helps in summarizing the most typical observation in a data set, especially when dealing with non-continuous data.
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
The median of the following data will be _________.
32, 25, 33, 27, 35, 29 and 30
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:
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.
