A 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?
2
Calculating the Mode of Wickets Taken
The question asks us to find the mode of the number of wickets taken by a bowler in 15 consecutive matches. The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.
Understanding the Mode in Statistics
In statistics, the mode is the value that appears most often in a set of data. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode at all (if all values appear with the same frequency).
Analyzing the Bowler's Wicket Data
The number of wickets taken in 15 consecutive matches are given as:
0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1, 2
To find the mode, we need to count how many times each value appears in this list. Let's list the unique values and their frequencies:
| Number of Wickets | Frequency (Number of Times Occurred) |
|---|---|
| 0 | 3 |
| 1 | 2 |
| 2 | 4 |
| 3 | 2 |
| 4 | 1 |
| 5 | 3 |
Looking at the frequency table, we can see which value appears most often:
- Value 0 appears 3 times.
- Value 1 appears 2 times.
- Value 2 appears 4 times.
- Value 3 appears 2 times.
- Value 4 appears 1 time.
- Value 5 appears 3 times.
The highest frequency is 4, which corresponds to the value 2. This means that the number of wickets '2' occurred most frequently in the given data set.
Identifying the Mode of Wickets
Since the value 2 appears more times than any other value (4 times), the mode of this dataset is 2.
Therefore, the mode of the given data is 2.
Revision Table: Key Statistical Terms
| Term | Definition | How to Calculate |
|---|---|---|
| Mean | The average of the data set. | Sum of all values divided by the number of values. $\left(\bar{x} = \frac{\sum x}{n}\right)$ |
| Median | The middle value in a data set that is ordered from least to greatest. | For an odd number of values, it's the single middle value. For an even number, it's the average of the two middle values. |
| Mode | The value that appears most frequently in a data set. | Count the frequency of each value and identify the one with the highest frequency. |
| Range | The difference between the highest and lowest values. | Maximum value - Minimum value. |
Additional Information on Measures of Central Tendency
The mean, median, and mode are all measures of central tendency. They help us find a single value that represents the center or typical value of a data set. The choice of which measure to use depends on the type of data and the shape of its distribution.
- The mean is sensitive to extreme values (outliers).
- The median is not affected by extreme values, making it useful for skewed distributions.
- The mode is the only measure of central tendency that can be used for nominal data (data that can be classified into categories but not ordered numerically). It is also useful for identifying the most common outcome in a dataset, as seen in this problem with the most frequent number of wickets.
In this problem, we specifically looked for the mode to find the number of wickets the bowler took most often across the matches.
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, 23The 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.
Given below is the marks obtained by 20 students in mathematics out of 30 marks.
7, 9, 12, 12, 13, 12, 14, 14, 14, 14, 15, 16, 17, 18, 18, 19, 20, 18, 20, 13. Then (2 × median — mode) of the data is equal to:
