Business Mathematics and Basic Statistics · Class 11 Commerce
Ch 4Measures of Central Tendency — Class 11 Business Mathematics and Basic Statistics, concept-first.
The arithmetic mean (usually called simply the mean) is the most widely used measure of central tendency — a single representative value for a whole set of data. Whether we are averaging test marks, daily sales, or the number of children in a set of families, the mean answers one simple question: if every observation w…
Key concepts
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Arithmetic Mean of Discrete Data
The arithmetic mean of a set of individual observations is ; the total of all values shared out equally among them.
Most relevant Q&A
- The ages (in years) of 6 employees in a small office are: 28, 34, 25, 40, 31, 36. Find the mean age.Free
- A football team's goals scored across 20 matches in a season are distributed as follows. Find the mean number of goals scored per match. | G…Free
- The marks obtained (out of 100) by 7 students in a class test are: 45, 52, 38, 60, 41, 55, 49. Find the arithmetic mean of the marks.Free
- A survey of 50 families in a locality recorded the number of children per family as follows. Find the mean number of children per family. |…Free
Chapter contents
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Arithmetic Mean — Discrete Data
The arithmetic mean (usually called simply the mean) is the most widely used measure of central tendency — a single representative value for a whole set of data.
Arithmetic Mean — Grouped Data
When data is grouped into class intervals (for example, wages grouped as ₹100–120, ₹120–140, and so on), we no longer know each individual observation — only how many observations fall into each inter…
Mode — Discrete Data
The mode of a data set is the value that occurs most often — the single "most popular" observation. Unlike the mean, the mode does not involve any addition or division at all; for a discrete frequency…
Median — Discrete Data
The median is the value that lies exactly in the middle of a data set once it has been arranged in ascending (or descending) order — half the observations lie at or below it, and half lie at or above…
Mean — Linear Transformation Rule
It is often useful to know how the mean of a data set changes when every observation is transformed in the same simple way — for example, converting every temperature from Celsius to Fahrenheit, every…
Exercises
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- Q9The ages (in years) of 6 employees in a small office are: 28, 34, 25, 40, 31, 36. Find the mean age.Free
- Q10A football team's goals scored across 20 matches in a season are distributed as follows. Find the mean number of goals scored per match. | G…Free
- Q11The weekly wages (in ₹) of 60 workers in a factory are grouped as follows. Find the mean wage using the direct method, and cross-check your…Preview
- Q12The number of siblings reported by 25 students in a class is distributed as follows. Find the modal number of siblings. | Number of siblings…Preview
- Q13The ages (in years) of 25 patients admitted to a clinic on a given day are distributed as follows. Find the median age using the cumulative…Preview
- Q14The mean weight of a group of students, measured in kilograms, is 52.4 kg. Weight is converted to pounds using the relation $y = 2.2x$ (wher…Preview
More questions
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- Example 1The marks obtained (out of 100) by 7 students in a class test are: 45, 52, 38, 60, 41, 55, 49. Find the arithmetic mean of the marks.Free
- Example 2A survey of 50 families in a locality recorded the number of children per family as follows. Find the mean number of children per family. |…Free
- Example 3The marks obtained by 40 students in an examination are grouped as follows. Find the mean marks using the direct method. | Marks | 0–10 | 10…Free
- Example 4The weekly wages (in ₹) of 50 workers in a factory are grouped as follows. Find the mean wage using the assumed mean method. | Wages (₹) | 1…Preview
- Example 5Using the same wages data as Worked Example 4, find the mean wage using the step-deviation method, and verify it agrees with the assumed mea…Preview
- Example 6A shoe shop recorded the sizes of shoes sold in a day as follows. Find the modal shoe size. | Shoe size ($x$) | 6 | 7 | 8 | 9 | 10 | |---|--…Preview
- Example 7The marks (out of 10) scored by 30 students in a class test are distributed as follows. Find the median mark using the cumulative frequency…Preview
- Example 8In Worked Example 3, the mean of a grouped marks distribution (classes 0–10 to 40–50) was found to be 27 by the direct method. If the marks…Preview