Class 9 Exam > Class 9 Notes > Mean, Median and Mode - Statistics, Class 9, Mathematics
Mean, Median and Mode - Statistics, Class 9, Mathematics PDF Download
ARITHMETIC MEAN
The average of numbers in arithmetic is known as the Arithmetic Mean or simply the mean of these numbers in statistics.
MEAN OF UNGROUPED DATA
The mean of n observations x1, x2, ...., xn is given by
where the symbol 
, called sigma stands for the summation of the terms.
Ex.14 The heights of 6 boys in a group are 142 cm, 154 cm, 146 cm, 145 cm, 151 cm and 150 cm. Find the mean height per boy.
Sol.
Ex.15 Find the mean of the first five multiples of 7.
Sol. The first five multiples of 7 are 7, 14, 21, 28 and 35.
MEAN FOR AN UNGROUPED FREQUENCY DISTRIBUTION
I. Direct Method
Let n observations consist of values x1, x2, ...., xn of a variable x, occurring with frequencies f1, f2, .... , fn respectively.
Then, the mean of these observations is given by :
Ex.18 The ages of 40 students in a class are given below :
Find the mean age of the class.
Sol. We prepare the table as given below :
Age (in years) Number of students 1;, xi
MEDIAN OF UNGROUPED DATA
Median : After arranging the given data in an ascending or a descending order of magnitude, the value of the middle-most observation is called the median of the data.
Method for Finding the Median of An Ungrouped Data
Arrange the given data in an increasing or decreasing order of magnitude. Let the total number of observations be n.
Ex.21 The marks of 13 students (out of 50) in an examination are:
39, 21, 23, 17, 32, 41, 18, 26, 30, 24, 27, 36, 9.
Find the median marks.
Sol. Arranging the marks in an ascending order, we have :
9, 17, 18, 21, 23, 24, 26, 27, 30, 32, 36, 39, 41
Here, n = 13, which is odd .
= Value of 7th term = 26.
Hence, the median marks are 26.
FAQs on Mean, Median and Mode - Statistics, Class 9, Mathematics
| 1. What is the difference between mean, median, and mode? |  |
Ans. Mean, median, and mode are measures of central tendency in statistics. The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of values. The median is the middle value in a set of numbers when they are arranged in order from lowest to highest. The mode is the value that appears most frequently in a set of numbers.
| 2. When should I use mean, median, or mode? | |
Ans. The choice of measure of central tendency depends on the nature of the data and the purpose of the analysis. The mean is typically used when the data is normally distributed and there are no outliers. The median is used when the data is skewed or when there are outliers that could affect the mean. The mode is used when the data is categorical or when the most frequent value is of particular interest.
| 3. How do I calculate the mean, median, and mode of a set of numbers? | |
Ans. To calculate the mean, add up all the numbers and divide by the total number of values. To calculate the median, arrange the numbers in order from lowest to highest and find the middle value. If there are an even number of values, take the average of the middle two. To calculate the mode, find the value that appears most frequently in the set of numbers.
| 4. What are some limitations of using mean, median, and mode? | |
Ans. One limitation of using mean, median, and mode is that they do not provide information about the spread or variability of the data. Another limitation is that they may not accurately represent the data if there are outliers or if the data is not normally distributed. In addition, the mode may not be defined or may be ambiguous if there are multiple values that appear with the same frequency.
| 5. How are mean, median, and mode used in real-life situations? | |
Ans. Mean, median, and mode are commonly used in many fields, including finance, economics, and social sciences. For example, the mean is used to calculate averages of financial data such as stock prices or GDP. The median is used to calculate the middle income or wealth of a population, which can provide insight into income inequality. The mode is used to identify the most common category in a survey or study, such as the most popular type of music or the most common health condition.
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