Page 1 Statistics Page 2 Statistics When a form of solid is converted into another one, surface area may change but volume remains the same. Hence, we equate the formula of volume of the other object, to the value (in numbers) of the volume of the original object to know the value of the new parameter. Calculate product of each “u? ” with corresponding frequency “ƒ? ” name it as “ u? ƒ? ” Arrange the data in increasing order Upper Limit Lower Limit Assume a mean ‘a’ of the given data values x? ’s : If the class intervals are odd in number then mid value of centermost class interval will be assumed as Mean. If the class intervals are even in number then the mid value of class interval having greater frequency will be assumed mean. Calculate the deviation of each mid value from assumed mean ‘a’ as d? = x? - a Calculate product of each “d? ” with corresponding frequency “ƒ? ” name it as “d? ƒ? ” Calculate sum of all ƒ? ’ s and “d? ƒ? ’s ” Calculate sum of all ƒ? ‘s and “ u? ƒ? ’s ” Mean of Grouped Data DIRECT METHOD ASSUMED MEAN METHOD STEP DEVIATION METHOD Calculate the product of each “x? ” with corresponding frequency “ƒ? ” name it as“ x? ƒ? ” Calculate sum of all ƒ? ’ s and “x? ƒ? ’s ” Calculate the range of data and then divide into class intervals of same class size. Calculate x? (Mid value) = (UL + LL) 1 2 Use to nd mean. x = a + ? d? ƒ? ? ƒ? Use to nd mean. x = a + ? u? ƒ? ? ƒ? ( ( x h Now, divide it by the class interval size ‘h’ , denote it as u? = x? - a h Use to nd mean. x = ? x? ƒ ? ? ƒ ? Mean of Ungrouped Data 1 2 3 x = n ? x i h - Class interval (size) x i - Observations n - Number of Observations x - Mean f i - Frequency STATISTICS 32 Statistics Page 3 Statistics When a form of solid is converted into another one, surface area may change but volume remains the same. Hence, we equate the formula of volume of the other object, to the value (in numbers) of the volume of the original object to know the value of the new parameter. Calculate product of each “u? ” with corresponding frequency “ƒ? ” name it as “ u? ƒ? ” Arrange the data in increasing order Upper Limit Lower Limit Assume a mean ‘a’ of the given data values x? ’s : If the class intervals are odd in number then mid value of centermost class interval will be assumed as Mean. If the class intervals are even in number then the mid value of class interval having greater frequency will be assumed mean. Calculate the deviation of each mid value from assumed mean ‘a’ as d? = x? - a Calculate product of each “d? ” with corresponding frequency “ƒ? ” name it as “d? ƒ? ” Calculate sum of all ƒ? ’ s and “d? ƒ? ’s ” Calculate sum of all ƒ? ‘s and “ u? ƒ? ’s ” Mean of Grouped Data DIRECT METHOD ASSUMED MEAN METHOD STEP DEVIATION METHOD Calculate the product of each “x? ” with corresponding frequency “ƒ? ” name it as“ x? ƒ? ” Calculate sum of all ƒ? ’ s and “x? ƒ? ’s ” Calculate the range of data and then divide into class intervals of same class size. Calculate x? (Mid value) = (UL + LL) 1 2 Use to nd mean. x = a + ? d? ƒ? ? ƒ? Use to nd mean. x = a + ? u? ƒ? ? ƒ? ( ( x h Now, divide it by the class interval size ‘h’ , denote it as u? = x? - a h Use to nd mean. x = ? x? ƒ ? ? ƒ ? Mean of Ungrouped Data 1 2 3 x = n ? x i h - Class interval (size) x i - Observations n - Number of Observations x - Mean f i - Frequency STATISTICS 32 Statistics Mode of Grouped Data Median of Grouped Data Mode of Ungrouped Data Median of Ungrouped Data Observe the greatest frequency ( f 1 ) and so the corresponding class will be modal class. Pen down ‘l’ = lower limit of modal class Pen down ‘l’ = lower limit of median class Note down the frequency of class preceding the modal class ( f 0 ) & the frequency of class succeeding the modal class ( f 2 ). Note down the cumulative frequency of class preceding the median class (c.f.) & the frequency of median class ( f ). Calculate class size ‘h’ as h = ( UL - LL ) Calculate class size ‘h’ as h = ( UL - LL ) Mode = l + x h ƒ 1 - ƒ 0 2 ƒ 1 - ƒ 0 - ƒ 2 ( ( Use this to nd mode. Observe that and Calculate n = ? ƒ ? n 2 Calculate the cumulative frequencies (c. f.) of all the classes. Observe the cumulative frequency just greater than and determine the corresponding class as median class. n 2 Use this to nd median. Median = l + - c ƒ ƒ ( ( n 2 x h It is the most frequent value of the obsevation i.e. the observation possessing maximum frequency. When n is even mean of the two centermost values median = { { When n is odd median = n 2 STATISTICS 33 Page 4 Statistics When a form of solid is converted into another one, surface area may change but volume remains the same. Hence, we equate the formula of volume of the other object, to the value (in numbers) of the volume of the original object to know the value of the new parameter. Calculate product of each “u? ” with corresponding frequency “ƒ? ” name it as “ u? ƒ? ” Arrange the data in increasing order Upper Limit Lower Limit Assume a mean ‘a’ of the given data values x? ’s : If the class intervals are odd in number then mid value of centermost class interval will be assumed as Mean. If the class intervals are even in number then the mid value of class interval having greater frequency will be assumed mean. Calculate the deviation of each mid value from assumed mean ‘a’ as d? = x? - a Calculate product of each “d? ” with corresponding frequency “ƒ? ” name it as “d? ƒ? ” Calculate sum of all ƒ? ’ s and “d? ƒ? ’s ” Calculate sum of all ƒ? ‘s and “ u? ƒ? ’s ” Mean of Grouped Data DIRECT METHOD ASSUMED MEAN METHOD STEP DEVIATION METHOD Calculate the product of each “x? ” with corresponding frequency “ƒ? ” name it as“ x? ƒ? ” Calculate sum of all ƒ? ’ s and “x? ƒ? ’s ” Calculate the range of data and then divide into class intervals of same class size. Calculate x? (Mid value) = (UL + LL) 1 2 Use to nd mean. x = a + ? d? ƒ? ? ƒ? Use to nd mean. x = a + ? u? ƒ? ? ƒ? ( ( x h Now, divide it by the class interval size ‘h’ , denote it as u? = x? - a h Use to nd mean. x = ? x? ƒ ? ? ƒ ? Mean of Ungrouped Data 1 2 3 x = n ? x i h - Class interval (size) x i - Observations n - Number of Observations x - Mean f i - Frequency STATISTICS 32 Statistics Mode of Grouped Data Median of Grouped Data Mode of Ungrouped Data Median of Ungrouped Data Observe the greatest frequency ( f 1 ) and so the corresponding class will be modal class. Pen down ‘l’ = lower limit of modal class Pen down ‘l’ = lower limit of median class Note down the frequency of class preceding the modal class ( f 0 ) & the frequency of class succeeding the modal class ( f 2 ). Note down the cumulative frequency of class preceding the median class (c.f.) & the frequency of median class ( f ). Calculate class size ‘h’ as h = ( UL - LL ) Calculate class size ‘h’ as h = ( UL - LL ) Mode = l + x h ƒ 1 - ƒ 0 2 ƒ 1 - ƒ 0 - ƒ 2 ( ( Use this to nd mode. Observe that and Calculate n = ? ƒ ? n 2 Calculate the cumulative frequencies (c. f.) of all the classes. Observe the cumulative frequency just greater than and determine the corresponding class as median class. n 2 Use this to nd median. Median = l + - c ƒ ƒ ( ( n 2 x h It is the most frequent value of the obsevation i.e. the observation possessing maximum frequency. When n is even mean of the two centermost values median = { { When n is odd median = n 2 STATISTICS 33 Median of Grouped Data Introduction to Statistics Mean of Grouped Data Cumulative frequency - Less Than Type Cumulative Frequency - More Than Type Scan the QR Codes to watch our free videos For nding median in an ungrouped data, please write the data in ascending or descending order rst. Mean – Mode = 3 (Mean - Median) approximately. An ungrouped data may not have a mode when there is no observation that occurs with highest frequency. PLEASE KEEP IN MIND UNGROUPED DATA GROUPED DATA ? ? If all the values are increased by a certain percentage/amount then mean also gets increased by the same percentage/amount. ? A set of grouped data modal class is the class with largest frequency. ? In a grouped data, the value of mean, median or mode will never exceed the respective class intervals. ? In the case of grouped data, make the class intervals continuous if they are not. This can be done by reducing the lower limit by 0.5 and increasing the upper limit by 0.5. ? ? STATISTICS 34Read More

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