Statics and probabilty
- 3. What is Deciles Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts. Formula D = 𝐊 10 th data ∗ (n + 1) Example: The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th and 100th percentiles if you were in the 99th percentile for a particular test, that would put you in the decile ranking of 10.
- 4. For Group data: That can be calculated from the following formula 𝐷1 = 𝑙 + 𝑤 𝑓 ( 𝑁 10 − 𝐶) 𝐷2 = 𝑙 + 𝑤 𝑓 ( 2𝑁 10 − 𝐶) 𝐷9 = 𝑙 + 𝑤 𝑓 ( 9𝑁 10 − 𝐶)
- 5. Where L= Lower boundary of the class containing 𝐷2 to 𝐷9 W=Class interval size of class containing 𝐷2 or 𝐷9 F= is the frequency of the class containing 𝐷2 or 𝐷9 N=number of values C=cumulative frequency
- 6. For Ungrouped data: 𝐷1 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛+1 10 𝐷2 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 2(𝑛 + 1) 10 𝐷3 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 9 (𝑛 + 1) 10
- 7. Quartiles The value which the arranged data into four equal parts are called ... And it represented by Q1,Q2,Q3 Understanding Quartiles To understand the quartile, it is important to understand the median as a measure of central tendency. The median in statistics is the middle value of a set of numbers. It is the point at which exactly half of the data lies below and above the central value.
- 8. Step to find Quartile Arrange the data in form of the lowest to highest Find the median of the data value. This is the value of Q2 Find the median of data value the fall bellow Q2.this is the value for Q1 Find the median of the data value that fall above Q2.This is the value for Q3
- 9. Quartile Formula First Quartile 𝐐1 = ( 𝐧+1 4 )𝐭𝐡𝐓𝐞𝐫𝐦 Second Quartile 𝐐2 = ( 𝐧+1 2 )𝐭𝐡𝐓𝐞𝐫𝐦 Third Quartile 𝐐3 = ( 3(𝐧+1) 4 )𝐭𝐡𝐓𝐞𝐫𝐦
- 10. How to find Quartile Q1,Q2,Q3 Data 1,2,3,4,5,6,7,8,9,10,12 n=11 Q2=? =(n+1)*50% =(11+1)*0.5 =6 The number which is at 6th position is Q2 which is 5 is median.
- 11. Inter quartile range The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie. That’s why it’s preferred over many other measures of spread Formula IQR= Upper Quartile − Lower Quartile
- 12. Central tendency A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. For example, suppose your earnings for the past week were the values shown in Table