Question

1. which of the distributions below has the larger standard deviation?

(a)distribution a
(b) distribution b
(c) the standard deviations are equal since the ranges are equal.
(d) the standard deviations are equal since both distributions are symmetric.

1. the five-number summary of the distribution of scores on the final exam in psych 001 last semester was min = 18 ( q _ { 1 } = 39 ) med = 62 ( q _ { 3 } = 76 ) max = 100. a total of 416 students took the exam. about how many students had scores above 39?

(a) 104 (b) 208 (c) 312 (d) 400

1. in a class of 100 students, the grades on a statistics test are summarized in the following frequency table.

the median grade is in which of the following intervals?
(a) 61 - 70.
(b) 71 - 80.
(c) 81 - 90.
(d) since the individual grades are not known, the median cannot be determined.

Explanation:

Question 8

Step1: Understand standard deviation

Standard deviation measures spread.

Step2: Analyze spread

Distribution A has more spread (points are more dispersed) than B.

Question 9

Step1: Recall five - number summary

\(Q_1 = 39\) (first quartile).

Step2: Calculate proportion above \(Q_1\)

Since \(Q_1\) is the 25th percentile, \(1 - 0.25=0.75\) of data is above.

Step3: Find number of students

\(0.75\times416 = 312\).

Question 10

Step1: Find median position

For \(n = 100\), median is at \(\frac{n + 1}{2}=50.5\)th position.

Step2: Cumulative frequencies

\(11+31 = 42\) (cumulative for 91 - 90 and 81 - 90). \(11+31+42=84\) (cumulative for 91 - 90, 81 - 90 and 71 - 80). 50.5 falls in 71 - 80 interval.

Answer:

A. Distribution A