CBSE Class 10 Mathematics Statistics Notes Set 01

CBSE Class 10 Mathematics - Statistics Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Class 10

Chapter : Statistics

Chapter Notes

Top Definitions

1. When a frequency distribution is obtained by dividing an ungrouped data in a number of strata, according to the value of variety under study, such information is called grouped data or classified data.

2. The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class to the frequency of the class.

3. In a less than ogive the upper limit of a class is plotted against its cumulative frequency as a point on the ogive.

4. In a ‘more than ogive’ the upper limit of a class is plotted against its cumulative frequency as a point on the ogive.

5. The mode for ungrouped data is the value that occurs most often.

6. In the case of a grouped frequency distribution a class with maximum frequency is called as the modal class.

7. A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution.

8. Distribution for which values of mean, median and mode are not equal is known as asymmetrical or skewed distribution.

Top Concepts

1. A cumulative frequency distribution can be represented graphically by means of an ‘ogive’.

2. The ogives can be drawn only when the given class intervals are continuous and if this is not the case then you don’t need to worry. All you need to do is simply make the class intervals continuous.

3. The ‘less than ogive’ is a rising curve.

4. The ‘more than ogive’ is a falling curve.

5. Direct Method of finding Mean

Step 1: First we find the mid values (also called class marks) of the intervals, denoted by ‘x’ or ‘m’

X=LowerLimit UpperLimit/2

Step 2: Multiply frequency with corresponding mid values obtained in

step1.

Step 3: Mean is calculated by using the following formula

6. Short Cut Method/ Assumed Mean Method

Step1: Find the class marks

Step2: Find the assumed mean (A) from the mid values

Step 3: Calculate deviation (d), d = x – A

Step 4: find the product of frequency with the corresponding deviations

Step 5 : Calculate mean by using the following formula

7. Step Deviation Method

Step1: Find the class marks

Step2: Find the assumed mean (A) from the mid values

Step 3: Calculate deviation (d). d = x – A

Step 4: After calculating deviations (d), we make one more column of values by dividing ‘d’ by ‘h’

Step 5: This is new value called step deviation (d’ or u) is multiplied with corresponding frequencies.

Step 6: Calculate mean by using the formula

8. The mode may be greater than, less than or even equal to the mean.

9. For finding the median we must arrange the given information i.e. the given data in increasing or decreasing order.

10. The last of the cumulative frequencies will be always equal to the total of all frequencies.

11. If the number of observations, n is even, so the median is the average of the (n/2)th observation and the (n/2+1)th observation.

12. The step deviation method will be convenient to apply if all the deviations (d’s) have a common factor

13. If class marks so obtained are in decimal form, then step deviation method is preferred to calculate mean.

14. The median of a grouped data can be obtained graphically as the x coordinate of the point of intersection of two ogives for the data.

15. The most commonly used method of central tendency is the mean. The biggest problem with mean is that it is effected by the extreme values one large or small number can distort the average. In that case the median is a better measure of central tendency while when the most repeated value or the most wanted one is required, and then mode is used.

16. The most frequently used measure of central tendency is the mean, because the mean is calculated by taking into account all the observations of a given data. And it lies between the smallest and the largest value of the data.

17. In general, Mean median and mode could be connected as follows

* Mean<=Median<=Mode

* Mean>=Median>=Mode

* Mode

* Mode>Median and Mean>Median

Top Formulae

Top Diagrams

1. Less than Ogive

2. More than Ogive

3. Median calculated graphically.

4. Symmetric Distribution

5. Asymmetrical or skewed distribution

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