Calculate Mean, Median, Mode, Lower and Upper Quartile. Also discuss the empirical relationships between quartile and percentile. Also calculate standard deviation for the data. 24 28 20 23 23 25 35 27 28 30 34 35 45 36 40 44 55 60 65 45 47 50
Answers
From the definition of median that it’s the middle point in the axis frequency distribution curve, and it is
divided the area under the curve for two areas have the same area in the left, and in the right. From this
may be divided the area under the curve for four equally area and this called quartiles, in the same
procedure divided the area for ten equally pieces of area is called deciles, finally where divided the area for
hundred equally pieces of area is called percentiles
Frequency
Data
Q1 Q2 Q3
A1
A2 A3
A4
Q1 = first quartile
Q2 = second quartile
Q3 = third quartile
Where:
A1 = A2 = A3 =A4
D1 = first decile
D2 = second decile
D3 = third decile
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D9 = ninthe decile
Where:
A1 = A2 = A3 = A4= . . . .=A10
P1 = first percentile
P2 = second percentile
P3 = third percentile
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P99 = ninety ninth percentile
Where:
A1 = A2 = A3 = A4= . . . .=A100
The same procedure for division is done for finding percentiles for any frequency distributed curve
To find the quartiles, or desiles, or percentiles we follow the same procedure to fined the median.
Arrangement the data in ascending form only.
If numbering arrangement of quartiles, desiles, and percentiles is fraction then its value is for the number
greater than it, if true number the value is the mean of its and the greater numbers