The diameter of the circle is 2”. What is the area of the circle
1 answer:
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The five number summary of the data is given below :
- Maximum = 157
- Minimum = 3
- Median = 47
- Lower quartile = 34
- Upper quartile = 65.5
- 157 is an outlier .
The data given :
3, 13, 15, 19, 21, 22, 25, 31, 33, 35, 35, 35, 37, 37, 38, 43, 43, 45, 46, 48, 49, 50, 50, 53, 56, 57, 59, 63, 65, 66, 70, 70, 74, 80, 82, 92, 98, 157
The five number summary for the data include ;
Maximum = 157
Minimum = 3
Median(Q2) = 1/2(n+1)th term
n = number of terms = 38
Q2 = 1/2(n+1)th term
Q2 = 1/2(39)th term = 19.5th term = (46+48)/2 = 47
Upper quartile (Q3) = 3/4(n+1)th term
Q3 = 3/4(39)th term = 29.25th term = (65+66)/2 = 65.5
Lower quartile (Q1) = 1/4(n+1)th term
Q1 = 1/4(39)th term = 9.75th term = (33+35)/2 = 34
Outliers :
Lower limit = Q1 - (1.5 × IQR)
IQR = Q3 - Q1 = (65.5 - 34) = 31.5
Lower outlier = 34 - (1.5 × 31.5) = - 13.25
Upper limit = Q3 + (1.5 × IQR)
Upper limit = 65.5 + (1.5 × 31.5) = 112.75
Outliers are values below or above the the lower limit or values above the upper limit.
157 falls above the upper limit, hence, 157 is an outlier. .
The boxplot of the data is attached below.
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