here are the scores of 12 students on a geography test.\n56, 60, 62, 70, 72, 74, 84, 84, 87, 87, 91…

here are the scores of 12 students on a geography test.\n56, 60, 62, 70, 72, 74, 84, 84, 87, 87, 91, 92\nnotice that the scores are ordered from least to greatest.\ngive the five - number summary and the interquartile range for the data set.\nfive - number summary\nminimum:\nlower quartile:\nmedian:\nupper quartile:\nmaximum:\ninterquartile range:

here are the scores of 12 students on a geography test.\n56, 60, 62, 70, 72, 74, 84, 84, 87, 87, 91, 92\nnotice that the scores are ordered from least to greatest.\ngive the five - number summary and the interquartile range for the data set.\nfive - number summary\nminimum:\nlower quartile:\nmedian:\nupper quartile:\nmaximum:\ninterquartile range:

Answer

Explanation:

Step1: Find the minimum and maximum

The minimum is the first number in the ordered list, and the maximum is the last number. Minimum: (56) Maximum: (92)

Step2: Find the median

Since there are (n = 12) data points, the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+ 1))th values. (\frac{12}{2}=6), (\frac{12}{2}+1 = 7). The (6)th value is (74) and the (7)th value is (84). Median: (\frac{74 + 84}{2}=\frac{158}{2}=79)

Step3: Find the lower quartile ((Q_1))

The lower half of the data is (56,60,62,70,72,74). Since (n_1=6) (number of data points in the lower half), (Q_1) is the average of the (\frac{n_1}{2})th and ((\frac{n_1}{2}+1))th values. (\frac{6}{2}=3), (\frac{6}{2}+1 = 4). The (3)rd value is (62) and the (4)th value is (70). (Q_1=\frac{62+70}{2}=\frac{132}{2} = 66)

Step4: Find the upper quartile ((Q_3))

The upper half of the data is (84,87,87,91,92). Since (n_2 = 6) (number of data points in the upper half), (Q_3) is the average of the (\frac{n_2}{2})th and ((\frac{n_2}{2}+1))th values. (\frac{6}{2}=3), (\frac{6}{2}+1=4). The (3)rd value is (87) and the (4)th value is (91). (Q_3=\frac{87 + 91}{2}=\frac{178}{2}=89)

Step5: Calculate the inter - quartile range (IQR)

(IQR=Q_3 - Q_1) (IQR=89-66 = 23)

Answer:

Minimum: (56) Lower quartile: (66) Median: (79) Upper quartile: (89) Maximum: (92) Interquartile range: (23)