find the 5 number summary for the data shown\n5 number summary:\nuse the locator/percentile method described…

Explanation:

Step1: Order the data

First, we order the data set. The data set is (5,13,15,25,34,46,51,54,64,76,87,94,99)

Step2: Find the minimum

The minimum value of the data set is the first value when ordered. So, (Min = 5)

Step3: Find (Q_1)

The formula for the locator of the first - quartile (L_{25}) is (L_{25}=\frac{25}{100}(n + 1)), where (n = 13) (the number of data points).

(L_{25}=\frac{25}{100}(13 + 1)=\frac{25\times14}{100}=3.5)

Since (L_{25}=3.5), (Q_1=x_3+0.5(x_4 - x_3))

(x_3 = 15), (x_4 = 25)

(Q_1=15+0.5(25 - 15)=15 + 5=20)

Step4: Find the median ((Q_2))

The formula for the locator of the median (L_{50}) is (L_{50}=\frac{50}{100}(n + 1))

(L_{50}=\frac{50}{100}(13+1)=7)

So, (Q_2=x_7 = 51)

Step5: Find (Q_3)

The formula for the locator of the third - quartile (L_{75}) is (L_{75}=\frac{75}{100}(n + 1))

(L_{75}=\frac{75}{100}(13 + 1)=\frac{75\times14}{100}=10.5)

Since (L_{75}=10.5), (Q_3=x_{10}+0.5(x_{11}-x_{10}))

(x_{10}=76), (x_{11}=87)

(Q_3=76+0.5(87 - 76)=76+5.5 = 81.5)

Step6: Find the maximum

The maximum value of the data set is the last value when ordered. So, (Max=99)

Answer:

(5,20,51,81.5,99)