Statistics is a branch of Mathematics that deals with data collection, analysis, interpretation, presentation and organisation. In AP Class 10 Maths Chapter 14 Statistics, we learn about the three kinds of averages mean, median and mode. Refer to this APÂ SSC 10th Class Maths Chapter 14 Statistics notes and solutions to understand the concept and prepare for the exams.
Mean, Median and Mode
Mean – It is the sum of values of all the observations divided by the total number of observations.
The mean for grouped data is calculated as follows:
Direct Method: [latex]\bar{x}=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/latex]
Assumed Mean Method: [latex]\bar{x}=a+\frac{\sum f_{i}d_{i}}{\sum f_{i}}[/latex]
Step Deviation Method: [latex]\bar{x}=a+(\frac{\sum f_{i}u_{i}}{\sum f_{i}})h[/latex]
Median – It is a measure of central tendency which gives the value of the middle-most observation in the data.Medianof a grouped data is calculated using the formula
[latex]Median=l+(\frac{\frac{n}{2}-cf}{f})\times h[/latex]Mode – It is the value among the observations which occurs most frequently. The mode for a grouped data is found using the formula
[latex]Mode=l+(\frac{f_1-f_0}{2f-1-f_0-f_2})h[/latex]Class 10 Maths Chapter 14 Statistics Chapter Questions
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- The following table shows the ages of the patients admitted to a hospital during a year:
| Age in Years | 15-25 | 25-35 | 35-45 | 45-55 |
| Number of Patients | 6 | 11 | 21 | 23 |
Find the mean of the data given above
Solution:
The class mark is found using the formula
[latex]Class Mark=\frac{Upper\,class\,limit-Lower\,class\,limit}{2}[/latex]| Age | Number of Patients ([latex]f_i[/latex]) | Class Mark ([latex]x_i[/latex]) | [latex]f_ix_i[/latex] |
| 15-25 | 6 | 20 | 120 |
| 25-35 | 11 | 30 | 330 |
| 35-45 | 21 | 40 | 840 |
| 45-55 | 23 | 50 | 1150 |
| [latex]\sum f_i=61[/latex] | [latex]\sum f_ix_i=2440[/latex] |
The mean is calculated as follows:
[latex]\bar{x}=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/latex]Substituting the values, we get
[latex]\bar{x}=\frac{2440}{61}=40[/latex]The mean is 40.
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