Question

A business statistics professor gives 100-point exams to two different sections of business statistics. The scores in one section, Section 001, of the class were 40, 50, 61, 63, 67, 74, 74, 76, 76, 78, 78, 80, 82, 86, 87, 87, 87, 88, 90, 90, 91, 92, 92, 93. The other class, Section 002, had scores of 67, 67, 68, 75, 75, 76, 79, 79, 80, 80, 80, 83, 86, 87, 87, 88, 89, 89, 90, 90, 90, 91.

Based on the interquartile range (IQR), which section’s exams were more tightly grouped?

The scores in Section 001 were just slightly more tightly grouped, based on IQR, with IQR for Section 001 of 13 and IQR for Section 002 of 15?

The Interquartile Ranges in both sections are exactly the same, with both being 15?

Both groups of data were equally grouped together?

The scores in Section 002 were just slightly more tightly grouped, based on IQR, with IQR for Section 001 of 15 and IQR for Section 002 of 13?

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The following are given for a set of values:
I.    The values ranged from 4 to 30.
II.   The median value was 14.
III. 25 percent of the values are less than or equal to a value of 7.
IV. 75 percent of the values are less than or equal to 20.

From the above information, the interquartile range for the data set is

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Given that a population of values is approximately bell-shaped with a mean of 25 and a standard deviation of 2, the approximate percentage of data values that is expected to fall between 21 and 29 is

Answer 1

Total no. of scores in Section 001 is 24

Thus, Q1 = Average of 6th and 7th observation = 74

Q3 = Average of 18th and 19th observation = (88 + 90)/2 = 89

Thus, IQR = 89 - 74 = 15

Total no. of scores in Section 002 is 22

Q1 = 6th observation = 76

Q3 = 17th observation = 89

Thus, IQR = 89 - 76 = 13

The scores in Section 002 were just slightly more tightly grouped, based on IQR, with IQR for Section 001 of 15 and IQR for Section 002 of 13

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Min = 4, Max = 30

Q1 = 7, Median = 14, Q3 = 20

Interquartile range for the data set = Q3 - Q1 = 20 - 7 = 13

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Given:

Mean,

Standard deviation,

The values between 21 and 29 lies within 2 standard deviation from the mean

i.e. P(-2 <= Z <= 2) = 0.9544

Thus, approximately 95.44 % of data values are expected to fall between 21 and 29