Question

A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online. Student Score Student Score A 26 F 89 B 93 G 81 C 89 H 58 D 92 I 92 E 71 J 96 (a) What is the range of data in this population? min (b) What is the IQR of data in this population? min (c) What is the SIQR of data in this population? min (d) What is the population variance? (e) What is the population standard deviation? (Round your answer to two decimal places.) min

Answer 1

After arranging the given data in ascending order, we get:

(a)

The range of the data = (Largest observation) - (Smallest observation)

= 96 - 26

= 70

(b)

IQR = Q₃ - Q₁

where Q₁ and Q₃ are the lower and upper quartiles respectively.

Now, since we have an even no. of data. Thus we divide the data (after arranging it in ascending order) into 2 equal parts. The median of the first half (the middle observation) will be Q₁ and the median of the second half (the middle observation) will be Q₃.

The first half of data : 26, 58, 71, 81, 89. Thus, Q₁ = 71

The second half of data : 89, 92, 92, 93, 96. Thus, Q₃ = 92

Thus, IQR = 92 - 71 = 21

(c)

SIQR = IQR/2 = 21/2 = 10.5

(d)

Now,

Thus,

(e)

Population standard deviation :

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