In this page we will explain the topics for the chapter 14 of Statistics Class 10 Maths.We have given quality Introduction to Statistics Class 10 Notes to explain various things so that students can benefits from it and learn maths in a fun and easy manner, Hope you like them and do not forget to like , social share
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- Flash back from IX Class Statistics
- Mean for Ungroup Frequency table
- Mean for group Frequency table
- Various ways to calculate mean
- Mode for grouped frequency table
- Cumulative Frequency chart
- Median of a grouped data frequency table
- Empirical Formula between Mode, Mean and Median

- Statistics deals with collection, presentation, analysis and interpretation of numerical data.
- Arranging data in a order to study their salient features is called presentation of data.
- Data arranged in ascending or descending order is called arrayed data or an array
**Range**of the data is the difference between the maximum and the minimum values of the observations- Table that shows the frequency of different values in the given data is called a
**frequency distribution table** - A frequency distribution table that shows the frequency of each individual value in the given data is called an ungrouped frequency distribution table.
- A table that shows the frequency of groups of values in the given data is called a grouped frequency distribution table
- The groupings used to group the values in given data are called classes or class-intervals. The number of values that each class contains is called the class size or class width. The lower value in a class is called the lower class limit. The higher value in a class is called the upper class limit.
**Class mark**of a class is the mid value of the two limits of that class.- A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an
**Inclusive or discontinuous Frequency Distribution**. - A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an
**exclusive or continuous Frequency Distribution**

Median is calculated as

Where n is the number of values in the data. If the number of values in the data set is even, then the

Greek letter ∑ (capital sigma) means summation

A survey was conducted by a group of students as a part of their environment awareness programmes, in which they collected the following data regarding the number of plants in 30 houses in a locality. Find the mean number of plants per house.

Mean = 172/30 = 5.73

In these distribution, it is assumed that frequency of each class interval is centered around its mid-point i.e class marks

This method can be very calculation intensive if the values of f and x are large.We have big calculations and chance of making mistake is quite high

(1) Prepare a frequency table with the help of class marks

(2) Multiply f

(4) Use the above formula and find the mean.

Find the mean by using direct method.

So, Mean would be

=698/10 = 69.8 kg

Where

a=> Assumed mean

d

This method is quite useful when the values of f and x are large. It makes the calculation easiar.In this method we take some assumed mean and calculate the deviation from it and then calculate mean using above formula

(1) Prepare a frequency table.

(2) Choose A and take deviations d

(3) Multiply f

(4) Use the above formula and find the mean.

The following table shows the weights of 10 children:

Find the mean by using Assumed Mean method.

Let the assumed mean = A = 71

So, Mean would be

=71-12/10 = 69.8 kg

Where

a=> Assumed mean

u

This method is quite useful when the values of f and x are large. It makes the calculation further easiar by dividing the deviation from common factor.

(1) Prepare a frequency table.

(2) Choose A and h and take u

(3) Multiply f

(4) Use the above formula and find the mean.

The following table shows the weights of 10 children:

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Find the mean by using Step Deviation method.

Let the assumed mean = A = 71 and h=2

So, Mean would be

=71+ (-6/10) 2 = 69.8 kg

(1)The mean obtained by all these three methods are same.

(2) The assumed mean method and step-deviation method are just simplified forms of the direct method.

Mode formula is given as

Where

l = lower limit of the modal class,

h = size of the class interval (assuming all class sizes to be equal),

f

f

f

The following table shows the ages of the patients admitted in a hospital during a year

Find the mode

Modal class = 35 – 45, l = 35, class width (h) = 10, f

Substituting the values in the Mode formula given above we get

Mode= 36.8 year

Cumulative Frequency chart will be like

The above table cumulative frequency distribution of the less than type. We can similary make it like below

The table above is called a cumulative frequency distribution of the more than type.

(1) For the given data, we need to have class interval, frequency distribution and cumulative frequency distribution

(2)Then we need to find the median class

(a) we find the cumulative frequencies of all the classes and n/2

(b)We now locate the class whose cumulative frequency is greater than (and nearest to) n/2

(c)That class is called the median class

(3) Median is calculated as per the below formula

Where

l = lower limit of median class,

n = number of observations,

cf = cumulative frequency of class preceding the median class,

f = frequency of median class,

h = class size (assuming class size to be equal)

Height (in cm) |
Number of girls |

Less than 140 |
4 |

Less than 145 |
11 |

Less than 150 |
29 |

Less than 155 |
40 |

Less than 160 |
46 |

Less than 165 |
60 |

To calculate the median height, we need to find the class intervals and their corresponding frequencies.

The given distribution being of the less than type, 140, 145, 150, . . ., 165 given the upper limits of the corresponding class intervals. So, the classes should be below 140, 140 - 145, 145 - 150, . . ., 160 - 165. Observe that from the given distribution, we find that there are 4 girls with height less than 140, i.e., the frequency of class interval below 140 is 4 . Now, there are 11 girls with heights less than 145 and 4 girls with height less than 140. Therefore, the number of girls with height in the interval 140-145 will be 11-4=7. Similarly, other can be calculated

Class interval |
Frequency |
Cumulative Frequency |

Below 140 |
4 |
4 |

140-145 |
7 |
11 |

145-150 |
18 |
29 |

150-155 |
11 |
40 |

155- 160 |
6 |
46 |

160- 165 |
14 |
60 |

So, n =60 and n/2=30 And cumulative frequency which is greater than and nearest to 30 is 40 , So median class 150-155

cf (the cumulative frequency of the class preceding 150 - 155) = 29,

Now by Median Formula

= 150 + [(30-29)/11]5

=150.45 cm

When we draw the graph for the cumulative frequency distribution of the less than type.The curve we get is called a cumulative frequency curve, or an ogive (of the less than type).

When we draw the graph for the cumulative frequency distribution of the more than type.The curve we get is called a cumulative frequency curve, or an ogive (of the more than type).

When we plot both these curve on the same axis, The two ogives willintersect each other at a point. From this point, if we draw a perpendicular on the x-axis, the point at which it cuts the x-axis gives us the median

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

5. It is the difference between the maximum and minimum values in data set.

7. The highest frequency class interval is .....class

8. Middle value of the dataset

1. Terms for number of times the event occurred in an experiment or study

2. It is a set of adjacent rectangles whose areas are proportional to the frequencies of a given continuous frequency distribution

4. Maximum frequency data in data set

6. Average value of a data set

(1)Frequency

(2)Histogram

(3)Cumulative

(4)Mode

(5)Range

(6)Mean

(7)Model

(8)median

**Notes**-
**Assignments** -
**NCERT Solutions**

Class 10 Maths Class 10 Science