find the mean, median, iqr, and standard deviation for the data listed below. games per world series: 4 7 6…

Explanation:

Step1: Calculate the mean

The data set is (4,4,4,6,6,6,7,7,7,7,7,7,7). The sum of the data is (4\times3 + 6\times3+7\times7=12 + 18+49 = 79). There are (n = 13) data - points. The mean (\bar{x}=\frac{79}{13}\approx6.08).

Step2: Calculate the median

Since (n = 13) (an odd - numbered data set), the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{13+1}{2}=7)-th value. Arranging the data in ascending order (4,4,4,6,6,6,7,7,7,7,7,7,7), the median is (7).

Step3: Calculate the first and third quartiles

The lower half of the data set is (4,4,4,6,6,6). The median of the lower half ((Q_1)) is the (\frac{6 + 1}{2}=3.5)-th value. (Q_1=\frac{4 + 6}{2}=5). The upper half of the data set is (7,7,7,7,7,7). The median of the upper half ((Q_3)) is the (\frac{6+1}{2}=3.5)-th value of the upper - half data set. (Q_3 = 7). The inter - quartile range (IQR=Q_3 - Q_1=7 - 5 = 2).

Step4: Calculate the standard deviation

The formula for the sample standard deviation is (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}). (\sum_{i = 1}^{13}(x_i - 6.08)^2=(4 - 6.08)^2\times3+(6 - 6.08)^2\times3+(7 - 6.08)^2\times7) (=( - 2.08)^2\times3+( - 0.08)^2\times3+(0.92)^2\times7) (=4.3264\times3 + 0.0064\times3+0.8464\times7) (=12.9792+0.0192 + 5.9248) (=18.9232) (s=\sqrt{\frac{18.9232}{12}}\approx1.26)

Answer:

Mean: (6.08), Median: (7), IQR: (2), Standard Deviation: (1.26)