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# Data array and frequency distribution

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• 1. DATA ARRAY AND FREQUENCY DISTRIBUTION
• 2. DATA ARRAY  Data: Numbers or measurements that are collected as a result of observations.  Array: An array is a systematic arrangement of objects, usually in rows and columns.  Data Array: Observations that are systematically arranged.
• 3. TYPES OF DATA There are mainly four types of statistical data:  Primary statistical data  Secondary statistical data  Qualitative statistical data  Quantitative statistical data.
• 4. POPULATION VS SAMPLE SIZE  Population: The “population” in statistics includes all members of a defined group that we are studying or collecting information on for data driven decisions.  Sample: The sample is a proportion of the population, a slice of it, a part of it and all its characteristics.
• 5. UNGROUPED VS GROUPED  Ungrouped Data: It is the data that you first gather. Ungrouped data is data in the raw.  Grouped Data: It is data that has been organized into groups known as classes. Grouped data has been 'classified' and thus some level of data analysis has taken place, which means that the data is no longer raw.
• 6. FREQUENCY DISTRIBUTION  Frequency: It is the number of observations following in some class.  Frequency Distribution: It is a listing of classes and their frequencies.
• 7. CLASSES  There is no thumb rule about the number of classes, but roughly it is suggested that the number of classes should be between 8 to 15.  Inclusive Classification: It is used for the classes like 55-57, 58-60, ……, 68-70. Both end points of the classes are included in the respective classes.  Exclusive Classification: It is used for the classes like 10-20, 20-30,……50-60. The 2nd end point is not included in the respective classes.
• 8. Such classes should be avoided. The gap between the classes is known as “height” an is denoted by “h”  The gap between class boundaries is known as class interval. 6163635958595556 6564646562626162 6169616364696667 6463625564655958 6566676462566259
• 9. Frequency Distribution Methods  Entry Table: By listing the actual observations  Tally Sheet: By using a tally column
• 10. Forming Frequency (Tally Sheet) fOBSERVATIONSCLASSES 4| | | |55-57 6| | | | |58-60 14| | | | | | | | | | | |61-63 12| | | | | | | | | |64-66 4| | | |67-69
• 11. Forming Frequency (Entry Table) fOBSERVATIONCLASSES 456, 55, 55, 5655-57 659, 58, 59, 58, 59, 5958-60 1463, 63, 62, 61, 62, 62, 61, 62, 63, 62, 61, 62, 61, 63 61-63 1265, 64, 64, 65, 66, 64, 65, 64, 64, 65, 66, 64 64-66 467, 69, 69, 6767-69
• 12. Class Boundaries and Mid Points fMid Points CLASS BOUNDARIES CLASSES 45654.5-57.555-57 65957.5-60.558-60 146260.5-63.561-63 126563.5-66.564-66 46866.5-69.567-69
• 13. Relative Frequency and % Frequency % FREQUENC Y RELATIVE FREQUENC Y fCLASSE S 0.10*100 =104/40 = 0.10455-57 0.15*100 =156/40 = 0.15658-60 0.35*100 =3514/40 = 0.351461-63 0.30*100 =3012/40 = 0.301264-66 0.10*100 =104/40 = 0.10467-69 100 %1.0040TOTAL
• 14. Cumulative Frequency and % C.F %C.F%fC.FfCLASS ES 10%10%4455-57 10+15 = 25%15%4+6 = 10658-60 25+35 = 60%35%10+14 = 241461-63 60+30 = 90%30%24+12 = 361264-66 90+10 = 100% 10%36+4 = 40467-69 100%40TOTAL